Yes, shoulder injuries/surgeries have left me extremely recoil-sensitive.
Yes, I can handle a 30-06 with stout loads. Don' t like it too much, though.
The biggest I have tried is the .340 Wby Mag (actually, it is the .375 H&H, but the .340 appeared to kick harder).
My upper range limit for recoil are the " standard" 7mm mags (Rem and Wby).