I may be ignorant but do not understand how any repeater could not be synchronised, mechanically speaking. The only prohibition I've read regarding the MK-103 was that it was at some point intended to be used as motorkanone in an Me-109K subtype but this was not possible because of its size and recoil concerns in the relatively light airframe and engine mount of the Messerschmitt (iirc it would rattle the engine too much but was tested on the ground).
Given the Ta-152 were still in the development phase and could be effectively constructed around different armaments installations to suit, and weight on their side I don't see any reason the MK-103 would not be fitted. As I understand it the Ta-152B-5 was a proposal derived of the Jumo engine reconnaissance version that had its airframe in common with the Ta-152C, which was in effect derived of the Ta-152B series but with fitment of the DB-603, hence the Ta-152B-5 and C-3 with same equipment but DB-603 motor were to be produced alongside the Ta-152C-1, H-1 and the B-reconnaissance version. By this stage the later, more capable versions of the Fw-190D using various Jumo and DB-603 types would be helping fill out squadron numbers in conventional aircraft, on the don't put all your eggs in the jet basket rule.
I realise that initially some work was required to perfect synchronisation for the MG-151 but I assume this involved as much sorting a reliable electrical interrupter to the wing roots of the Fw-190A, which could be readily adapted to any other electrically fired gun type. I don't think it was something specific to the MG-151 itself, just its type. Hence I can see no logical reason of a mechanical mind, that an MK-103 or any other repeater weapon cannot be interrupted for synchronisation given that a working linkage system for the gun placement is already developed previously. Both the MG-151 and MK-103 are electrically fired IIRC (the MK-103 basically an electrically fired version of the MK-101).
So then the problems could only be ones of recoil concerns and weight distribution. I do not think these much of an issue with the Ta-152 because weight distribution was still being sorted for improved low speed stability, most particularly in rear fuselage equipment and fuel tankage which were unresolved. I should think heavier guns in the wing roots might've actually helped. As it was it seems the MW-50 installation was moved to replace the inner port-wing fuel tank and reduced in size to get rid of some weight in the rear fuselage, and pilots were told not to put fuel in the rear fuselage tank due to similar instability you get with a fully loaded Mustang. I believe the production Ta-152B/C was to have the rear fuselage fuel tank removed also, to leave only the front tank and wing tanks (where the Fw-190 series has no wing tanks but front/rear fuselage tanks).
If someone was telling you it was impossible to synchronise the MK-103 the statement itself lacked credibility in the first place. I suggest they then attempted to confuse you by suggesting that "historically it was never done" which you have certainly proved wrong with good photographic evidence. Nicely done.
I usually like to ask for a mechanical reason something can't be done and therefore was never done. I suggest postwar enthusiasts can be a little conservative about what has been tried out in wartime conditions and like to neatly categorise something inherently anarchistic to some degree. Regulations and guidelines are more often than not a work in progress and even retroactive to actual fitments and conditions unexpectedly performed in wartime, or tried out in the field on some combination of desperate inspiration.
For example even aircraft model variants are only a general guideline, every aircraft is individual and a more accurate classification is by production series then individual modifications and flight condition, inevitably one arrives at the point that each specific tail number really represents a unique aircraft and many were freely modified in the field or by the factory to various squadron specifications at various times, differing fuel qualities and servicing facilities, etc.
Just to proclaim "all aircraft of this model had these specifications" is I think a mistake, let alone that something quite mechanically sound, possible and available was never done even if only loose references suggest it might've been.
To form such an absolute argument you'd have to track the history and records of each individual aircraft in the series. People who say which modifications were and were not performed seem to rarely have gone to these lengths in my experience.