It's true that the FG42 was uncontrollable in full-auto fire, but I'm not sure how I'm making your point for you. Yes, the FG42 was uncontrollable in full-auto model, but this is because of its full-power cartridge and not because of its low bore axis. I submit that the FG42 would be even more uncontrollable in full-auto model with a higher bore axis.
And this problem is not confined to the FG42. All of the phase III battle rifles, whatever their method of operation or layout, are uncontrollable in full-auto model. The FAL (relatively high bore axis with pistol grip and gas operation), G3 (straight-line construction with pistol grip and roller-delayed blowback operation), StG57 (straight-line construction pistol grip and roller-delayed blowback operation), and M14 (relatively high bore axis with rifle stock and gas operation), for example, are all uncontrollable in full-auto mode. It is not their layout or method of operation that causes them to be uncontrollable. Rather, it is that they are all chambered for full-power rifle cartridges instead of intermediate/assault rifle/carbine cartridges.
Incidentally, the FG42's chambering for the 7.92mm Mauser round was a specific design feature and not a miscalculation. At the same time the Luftwaffe was developing the FG42, the Wehrmacht was developing the MKb42(W) and MKb42(H). The MKb42(W) and MKb42(H) were chambered for the 7.92 x 33 kurz round, and this round was available when the FG42 was being developed. But the Luftwaffe specifically rejected the kurz round and specified the full-power 7.92 Mauser round because of bitter experience with British BREN gunners during the invasion of Crete. The British were able to engage the Fallschirmjager at ranges up to 1000 yards away. Because of this experience, the Luftwaffe specified the full-power round for what it believed was the future of battle rifle development.
Whether you or I agree with this call is unimportant. What matters more I think is that the call was made from battle experience, with deliberation and judgment, and not through whim or caprice or fad. The Americans made the same call later with the M14 and in ramrodding the .308 toward NATO standardization, so the Luftwaffe was not alone.
The StG44 may be more controllable in full-auto mode than the FG42, but is this is a valid criticism of the FG42? I don't think so. What the StG44 gains in controllability it loses in power. The StG44 is not a true rifle. Sure, it's an "assault rifle", the first of its breed, but is it really a rifle? I don't think so. I rather like Jeff Cooper's classification of the StG44 and its progeny as "battle carbines" rather than "battle rifles". Note that when Haenel and Walther first developed these types of weapons, the original classification was "MKb42" and not "G42". The Wehrmacht properly classified these weapons "machine carbines", as they were less powerful than true "machine rifles" and more powerful than "machine pistols". I think the original classification the Wehrmacht used is more accurate.
So I think the FG42 still stands as a suitable example of how to reduce muzzle jump and attenuate felt recoil. To make the FG42 as low-recoiling and controllable as possible, the designers utilized gas operation, a straight-line construction with the bore axis bissecting the buttstock, a telescoping buttstock that was buffered, and a huge muzzle brake. Features such as these reduce muzzle jump. They do not enhance muzzle jump. Without these features, the FG42 would be even more uncontrollable in full-auto mode.
This reminds me of another weapon utilizing the fishtail buttstock design. The American M60 is an unsuccessful attempt to utilize the FG42's method of operation with the MG42's feed system. But the M60 also copied the straight-line construction and buttstock layout from both the FG42 and MG42.