My PT22 from 1998 runs flawlessly on CCI MiniMags and Federal AutoMatch. Those are all I've run through it. Small blowback guns need quality ammo.
As a trainer for a LCP-sized gun, the Jimenez J/A-22 runs real close. It is, however, a single-action, striker-fired gun instead of a hybrid-DAO like the LCP (I) is. I have its predecessor, the Jennings, from back in 1987, and it's actually a nifty little shooter. I'd never carry it, though, due to concerns over loaded-chamber carry and the fact that I own more-powerful guns in the same size category (Taurus TCP in .380 and Kel-Tec P32.)
For pocket-carry, you're wise to avoid the Phoenix. It's a fun shooter, but is very heavy, very sharp-edged, and complicated by something like 64 passive and manual safety features.
The Walther TPH runs at the bottom end of the size range for quality .22 pistols, and at the top of the range for price.