sounds as if ur most likely culprit is the clutch n drum system of the trans, sounds as if ur gettin intermittent line pressure thru ur valve body....line pressure is what causes ur clutch packs in an auto trans to lock up, low or intermittent pressure will not allow the drums to lock up properly or at all in the absence of same.
if this was not a NEW tran, or was a rebuild, i suggest u have it redone, most likely there is gum and or varnish somewhere in the trans that is corrupting proper line pressure....BTW a 350 engine makin 375hp is NOT a mild engine, mild is AT OR BELOW 1hp per cube....LOL...but keep the mild attitude about it, that way ur always encouraged to seek even more power...