Regarding your questions, my opinions are as follows:

16 gauge frame size would work for conversion to .450/.400, but 12 gauge is still preferable, because you want to have completed rifle which balances well, with most weight between hands when holding it for firing, thus 12 gauge is still best for this caliber. 16 gauge is more suitable for 9.3 x 74R, .303 British, or similar. 20 gauge mag. 3" shotgun is suitable for 9.3x74R, as explained above; my original conversion by Francotte proving that point, giving a very slim, trim, lightweight 9.3 that is still comfortable to shoot, though 16 gauge gives a slightly heavier 9.3x74R; even more comfortable to shoot--more control of recoil.

12 gauge is most preferable for .405, .450/.400, and even more so for .450 3" or 3 1/4"; but is too light, too small, for conversions to .500. Good old 1960s-1970s vintage Spanish 10 ga. 3.5" mags. with Greener crossbolt are suitable for .577 full nitro, but a bit too heavy for conversion to .500 NE. I once measured carefully, the action of a great old British boxlock .577 N.E., and found it to be almost identical in size, except for depth below watertable, to these Spanish boxlock 10 ga. mag. actions. I have now made four conversions on them to .577 NE successfully, and know a good gunsmith friend who has done same conversions on them. Ellis Brown almost exclusively, I think, has used German shotgun conversions, successfully, and I have done many myself. My last one was 12 ga, Sauer to .500/.416 Rigby, a caliber I have come to love. Thus, your 12 ga. Merkel or Sauer would be especially suitable as specified here. Your 12 ga. Aya less so, due to fact that it has no third fastner-no crossbolt. It may work, but may not over time hold up as well as good German action with crossbolt. I have never used a shotgun action for conversion, that had no crossbolt, so I cannot for sure speak with certainty about their use. As Brown explains in his book, a crossbolt is good insurance for more structural integrity on an already compromised shotgun action to double rifle conversion, especially on heavy recoiling calibers. One simply cannot compare a modern alloy steel action frame having no crosbolt on double rifle, with a classic old shotgun action frame made from mild steel (which most were made from), having no crossbolt--that is mixing apples with oranges. Modern alloy steel, having many times the structural strength of common mild steel, needs no crossbolt, now well proven over time. This isn't true at all with old actions made from mild steel, usually color case hardened---the case hardening adds very little or more likely NO structural strength to such actions.