Probably it feels that the 0.22" gun is gentler, in reality it isn't. Recoil energies are poportional to ME's, if a gun outputs more ME, it also outputs more Recoil energy. Humans are bad "measurement machines" if anything takes longer, we feel it smoother.
I have nothing against HW guns, but if I were to deviate from Diana, I would go for a GasRam gun, whatever the maker. If I remember correctly it's the RX2 the one that is GasRammed. Apart from that nothing will make me deviate from Diana.
I understand the psychological end of the power equation, and a 350 is deffinitely powerful, but rather than scope it, I would advise you to start shooting with a peep sight. This reduces the possible problems and allows you to concentrate on shooting well, not on problem solving.
Your guns perform admirably well, we are not so blessed here at almost 9,000 ft above sea level.
JMHO
Un Abrazo!
Héctor