elimination question in final third of a 48 player tournament

[SeattleJake]

I was under a bit of scrutiny late in a live game, when I raised from the button forcing the small blind out of the pot with the big blind all-in.

Here's the scenario: Top 12 pay, 15 players left. Blinds are at 800/1500, but BB has only 600 in chips. I'm about 4200. SB has me covered. I'm Button with J7s, a horrible hand but still 50% against a random hand.

My thinking was that there were two important things for me to consider in that instance. First, that it's going to be worse for me to have SB win those chips than it would be for BB to win them, and better still for me to win them myself, as I have less than the average chip stack and the blinds are going up fast. Second, that considering my expected value from the play, it seemed the best option.

Call
30% chance of winning
2200 in the pot
800 cost to win 660
-140 expected value

Fold
0% chance of winning
1400 in the pot
0 cost to win 0
0 expected value

Raise
50% chance of winning
1800 in the pot
400* cost to win 900
+500 expected value

When I raised SB out of the pot, I grabbed 200 making my cost only 400 with 50% equity in a 1800 pot. If I had a larger stack, then folding would have been the better option. If I had a better hand, then calling would have been the better option. But as it was, I thought it was absolutely the right play.

A couple important points are missing from making this a standard elimination play. First, that I wouldn't have just called the hand -- so in effect BB had just as much chance against my hand as the random hand SB has. Second, that this way I increase my chances of making it to the final table instead of increasing my SB opponent's chances. If I had had a calling hand, or if I had had a larger chip stack, then calling and checking down to eliminate the player may have been correct, but neither of those were the case. But maybe not tripling up BB, coupled with my crappy hand, should have been enough to make me fold.

So in retrospect, my decision may have been an inexperienced one, so I'd like whatever advice someone can give.