I've done everything as a 30/30 STR spec warrior except Coil 2 (My main job is dragoon). A few complaints on Leviathan Ex my health pool was "low", but outside of that no issues. I don't see 30/30 STR being much of a problem in Coil 2 either (up to turn 8 anyway...haven't tried 9 yet).

Rafflesia doesn't hit particularily hard. Melisune and her adds aren't too terrible (unless offtank winds up with two dancers). Avatar would be tricky for a solo, STR spec tank, but I believe it was SE's intent for this to be a two tank encounter that the players found a way around. STR offtank + STR accessories can do well here.