I think the baby Martini .25-20 is doable & has been done quite often. My wife's Westley Richards in 298 Minex is, I'm quite sure, a joy to shoot, but I only get to cast bullets & load for it. It is essentially a .32-20 case using a 140 grain bullet measuring 0.300".
I've had a few .22 Hornets, 1 on a #2 SMLE, a couple on baby Martinis and my current Ruger #1. Never much cared for the .20 calibre anything. It's bothersome enough to load .22 Hornets with my sausage fingers, never mind a .20, much less a .17.
Re: 25 acp in the Stevens Favourite
It's always been an annoyance to me that there isn't a rimmed .25 case of about that size to use in Stevens' or Cooey rifles; just the old rim-fire cases. Sort of a smaller version of a .32 S&W.
Re: Cadet in 257 Maximum (necked down 357 Maxi) It's a hot little combination.
Is it a gently-tapered old-style cartridge or is it a sharp-shouldered bottleneck cartridge? I tried googling it, but nada.