To be fair, the only consistency I see is that the bad beats are becoming an issue because they're either a)Crippling you or b)Busting you out of the tourney.
The only way to offset the bad beats is to chip up. And usually, the more aggressive style of play is what gets you awarded with both more small pots than the average player, and also rewards you when you're pushing all in with a monster, and the second nuts calls you as they think you're bluffing
It seems to me like you're somewhere in the Tight-Aggressive to Tight-Passive type of player. This strategy is usually successful if you're a cash game player (Tight Aggressive in No Limit, Tight-Passive in Limit), but given the circumstances, you really do have to take a bit more risks midway through the tourney.
Understand that in a freeroll, the motivation to gamble it up is sooooo much higher than in a regular buy-in tourney. You can either choose to exploit it by setting tricky traps and trusting your reads, or, you can get your hands dirty and be one of the maniacs who can steal pots here and there.
In freerolls, I would definitely veer more toward a looser style of play, more between Tight-Aggressive and Loose-Aggressive.
But all in all, I do agree with vanquish's comment. There's no more advice you need if you got all your chips in with the best hand.
Good luck at the tables.