TAG doesn't mean to only play premium hands, especially in an MTT. Early on, sure, but once the blinds start going up, you want to use the tight image you've built to steal some blinds with not-so-great hands. If you're in late position with an 87s and nobody's come in yet, it may be a good time to raise 3 or 4 BBs. If you can steal the blinds 4 times every 3 orbits, (not to mention what you accomplish with your actual strong hands) you'll actually be profitting and building your chip stack instead of letting it sink. Also, you can't let your stack get so low that you have to push all-in UTG with only 5 BBs, if you can help it. You probably waited far too long to go all-in. You don't always have to be pushing in with premium hands when you're shortstacked. If you aren't getting dealt any decent pairs or high cards, look for situations where you're in late position with a hand that's unlikely to be dominated, like 68 or something (preferrably with at least 8 or more big blinds, or else you're going to get called too often) and consider pushing there. Even if the BB wakes up with AK and calls you, you're going to win 35-40% of the time.
If you haven't read Harrington on Hold 'Em volume 2 about M and Q and the different zones relating to the size of your stack, I strongly advise you do so, because it sounds like it will help you tremendously. If you have, maybe read it again to refresh.