Just push pre-flop.
I disagree with yours pre-flop 3bb raise: BB has a healthy stack and would probably call with an wide hand against which your 88 would be quite vulnerable post flop. Plus it would be enough an single caller to estimulate several players into the hand against who in most of the time you would be playing with a mid pair and the herculeal task of make all them fold. Finally 300 chip was a quite stab on yours short stack considering the fact that most of the time you will miss the set. Just imagine if Co call or Bu calls, prompting SB and BB into the pot? Now if flop comes Ah9c7h, what would you do with yours mid pair against 3 players?
Then you managed to get yourself heads up with a flopped full house, very nice. But after villain calls your bet on the turn with the J and the river brings the K, what hand did you supposed he was holding? AQ, AT? Honestly that J and then the K and player 2 still calling confidently...
Anyway, push pre-flop when raise represents a sizable portion of your stack seems for me the right play here.