Perhaps Otto Carius, a Jagdtiger company commander, said it best in his description of his vehicles. "Despite its 82 tons, our Hunting Tiger didn't want to act like we wanted it to. Only its armor was satisfactory, its manoeuvrability left a lot to be desired. In addition, it was an assault gun. There was no traversing turret, just an enclosed armored housing. Any large traversing of the main gun had to be done by moving the entire vehicle. Because of that, transmission and steering differentials soon broke down. That such a monstrosity had to be constructed in the final phase of the war made no sense at all."
In the final analysis, the roughly 70 Jagdtigers that were constructed were design failures in a number of areas and successful in only a few. The AFV was too heavy and cumbersome on the battlefield and proved not only difficult to get to the fighting, but almost impossible to recover afterward. Although when the weapon system could be brought to bear on an opponent the results were often devastating, out-manoeuvring the Jagdtiger was a relatively easy task for Allied AFVs, as long as they could stay out of its sights.
Frank De Sisto reports:
The 8.8cm Jagdtiger was discussed briefly by Tom Jentz at this year's  AMPS convention, during his seminar.
According to documents he uncovered, it was not a shortage of 12.8cm guns, but the MOUNTS.
Some minutes from wartime meetings were discussed by Tom and I believe he said 4 vehicles were fitted or considered for fitting with 8.8cm guns, and if memory serves, they may even have been issued.
Jentz says 4 were built in April with 17 more planned for April, but whether they made it into the field or not before being blown up at the factory as most accounts describe is the sore point.
There were supposedly a couple of independent SS led kampfgruppes outside the two main Bttns. of 512 and 653, running small numbers of Jagdtigers in the closing weeks also - eg. sSS.Pz.Abt.511 (formerly 501 - 1st SS LAH) ran 6 JTs in the last month in Austria etc. See p.267 "TIC 2" by Schneider and p.565-6 "Michael Wittmann and the Tiger Commanders of the LAH" by Agte. Plus I've heard unconfirmed claims from others that 17.SS "Gotz von Berlichingen" also had a KG with small numbers plus others with the odd vehicle attached. So who knows what was actually fielded and who had what at the end?
Jagdtiger was built in the Nibelungenwerke in late April/early May 1945 and they were commandeered by Waffen SS units hell-bent on continuing the fight. The Jagdtigers operational on April 30th 1945 went with the LAH battlegroup to St. Pälten with 4 vehicles, two crewed by members of sPzJgAbt 653, two crewed by the "unknown unit", which was probably from sPzJgAbt 512. The remaining functional vehicles were commandeered by another SS-battle group, perhaps of 2nd SS Panzer-Division, on May 4th 1945 and moved north in time to be put in the line during the final Russian offensive in Poland starting on May 6th, forcing Army Group Mitte out of Poland between May 8th and May 9th. The 8 unfinished Jagdtigers remaining in St. Valentin was blown up on May 4th 1945 as described in ‘The Combat History of German Heavy Anti-tank Unit 653 in World War II’ By Karlheinz Münch’s book.
So I'd say without further info, it’s not beyond the realms of "possibility" that a few 88mm versions "could have" trickled out right at the end especially if they jumped ahead in the run eg. the Fgst. no. on the 88mm one yet the No. on Kubinka's late 128mm version is 305083?
According to Wolfgang Schneider's "Elefant-Jagdtiger-Sturmtiger: Rarities of the Tiger Family", the 88mm gun was modified to fit the Jagdtiger (this modification being known as the PAK43/3, Version D), the gun being so modified by Hallesche Maschinenfabrik of Lippstadt. They delivered the weapons to the Nibelungen Works where the vehicle was being built beginning in 1944. Of the 74 Jagdtigers built, Schneider says there is no record of how many of them left the factories armed with the 88mm gun.
Given that the 88mm was merely a stop-gap measure to arm the Jagdtiger until 128mm guns were forthcoming, such a low number would seem to justify your reasoning and debunk the idea that 20 such vehicles rolled off the lines. One would wager that as soon as 128mm guns were to be had, they took precedence over the 88s.
I'm assuming something however, in that you are referring to the gun mount itself and not the gun. If the mount for the 88 read 7 of 20, then two things could be considered. First, that, yes, 20 mountings for the 88mm were produced (as a lot I'm sure). The other issue would be the mounting was a lot of 20 for the 128mm. The test would be to compare the gun mount of your machine with the 88 to one which mounted the 128mm. Schneider's text makes no mention of just what the modifications to the 88mm were...was it a modification of the gun or to the mount. I'm inclined to say the 88mm was modified to fit the gun mount meant for the 128mm. This would have prevented the factory from having to make a mount just for the 88mm and waste precious materials in doing so. With the 88mm suited to fit the 128mm mount, the factory can continue to build the one type of vehicle and use whatever gun happened to be available to them. Again, the acid test would be to compare the mountings of the two variants.
One would be hard pressed to locate a photograph of a Jagdtiger with the 88. The length of the gun tube for the 88 is about two inches shorter than the 128mm and if it shared the same mantlet as the 128 armed variant, without being able to see the breech, you'd be hard pressed to tell them apart. I checked my sources and examined the photographs and came up dry. Most of the photos I have show spiked Jagdtigers which, of course, ruins the weapon and with ammunition cook-offs, pretty much obliterates the superstructure and everything within it. All the others show the 128mm armed vehicle that I am able to discern.
The soft metal plate you found on the vehicle:
SonderKraftFahrZueg 185s 04/45 Nummer 05 F??Gb
This is indeed the Sd Kfz 185, the 88mm armed Jagdtiger according to the listing of Sd Kfz numbers I have from Peter Chamberlain's "Encyclopaedia of German Tanks of World War II". The "s" is a mystery though as I can find no data on that particular letter as it related to Sd Kfz nomenclature. Chamberlain does point out that Sd Kfz numbering was far from perfect and sometimes were not consistent. Of note, Chamberlain says that no 88mm armed Jagdtiger went into production (keep in mind his book came out in 1978).
The exact number of Jagdtigers produced may never be known. Sources differ from one another in production numbers, Chamberlain having 61 produced in 1944 and a mere 16 produced in 1945. Of course, Schneider claims 74 produced. I would hazard to guess that some of the other numbers may include those still on the factory floor by wars end.
Keep in mind though, that by the closing weeks of the war, record keeping went out the window or went up in smoke to prevent the information from falling into the enemy’s hands. Schneider has the Nibelungen Works and the Steyr-Daimler-Puch facility at St. Valentin (unless the two are one and the same...Schneider makes no differentiation). If Steyr-Daimler-Puch could be contacted, perhaps they have records in their archives (since this company is still around today)...in much the same way that Dornier still has the plans and data on their WWII aircraft (which allowed them to rebuild Do335 "Pfiel" Wk.Num. 102). It’s a long-shot...but it might pay off.
It’s interesting that it appears that the vehicle left the factory in April of 1945, going by the Sd Kfz plate. Given the end of the war was weeks away, perhaps it seems that, in an effort to put out vehicles (which in turn might account for the poor welds), 88s were used from those sent to the factory in 1944. It was Hitler’s desire that the 128mm gun be used, the 88 only being used until 128mm guns could be had. Since Krupp was building the 128mm PaK44 L/55 (which was later called the 128mm PaK80 ) at their Breslau facility...Allied bombing and Allied ground action would surely have influenced delivery of the weapon to the Jagdtiger plant, especially at this late stage of the game. If spare 88mm guns were lying about the factory floor, you can make a safe bet that they would be installed. While your source quoting that four 88 armed Jagdtigers rolled off the lines in 1944, which would make sense given the lack of 128mm guns and the need to put the vehicle into the field...there is certainly an argument for vehicles coming off the line at the close of the war when, most likely, delivery of 128mm guns was sketchy at best and orders or no orders, guns on-hand were to be put to use.
One interesting identifier of late model Jagdtigers is the drive sprocket. To allow the new tracks to be fitted, every other sprocket tooth was removed by torch.