Sorry, the .38 Special +P sucks, even in an airweight gun. Shooting .357 Magnum with full case loads of H110 isn't the best practice for the airlites, but you can easily do a lot better than .38 +P.
In my 442, I could get never get a 125 gr. bullet faster than 850fps.
In a 340 PD, I could load a 125 gr. anywhere from 700 to 1400 fps.
To match the performance of a 9mm compact auto for penetration and expansion, you'd need to drive it to about 1100 fps. This is still a lot of recoil in an airlite, but I would take 1000 fps over 850 fps any day.