In order to win a poker tournament you are going to have to win a few races - it is extremely difficult to get deep into a satellite like the one you described without racing unless the deck is hitting you fairly solidly. There are, however, a few tricks to chipping up when you are card dead that i like to use. Mainly, I play position, but if that fails (as it often does if you raise on the button because it is easy to read) I like to disguise my bluff by making the raise in early-middle position with connectors (78 is an ideal hand for this move.) Take advantage of the Gap Concept through this move, and hopefully you will steal some blinds. If you do raise with the connectors, however, there are still escape routes:
1. You hit your hand. They don't expect it because they are putting you on a pretty strong hands such as a couple of high cards at least.
2. If you miss your hand, there is usually a high card on the flop that you can represent by leading out on the flop.
Of course this isn't a guaranteed chip up, I do often find myself losing 1/5 of my stack on plays like this.
If even after you disguise your steals by raising in earlier position and you are still getting reraised, sit and wait for your hand to push your chips in with. Also, watch and see how the villain re-raiser acts if the person they re-raise 3 bets. If they fold this could be a good way to chip up quickly (also risky!) If you do have the goods on a 3 bet, make sure you show them your hand, it could help to get them to fold a little more often.
Of course your M plays a HUGE role in knowing when you have to make these steals. If you are in the green or yellow zone you don't have to make this play, in fact I would say that you shouldn't. Once you get in the orange zone with an M of 10 or less, that is a pretty ideal time to start getting more aggresive.
If all else fails and you do not want to race, the squeeze play is also another option.
Most importantly though, when you do hit your hand (i.e. a set) you need to maximize your value on the hand. I don't know how experienced you are at playing poker, but value betting is KEY. You need to extract as many chips as you can from your opponent when you are certain (or fairly certain) you have the best hand. The "rope-a-dope" slow play is a fair move to extract chips, but against a tight player (or a super-aggressive player for different reasons) betting out will often get more chips. I like to bet 1/3 of the pot or so(as high as 1/2 as low as 1/4) If they fold you weren't likely to get any more chips anyway. Against the table you were descibing, betting out your sets would seem like a great play because you had some super LAG players at your table. I often see players reraise my tiny bet all in with trash and i quickly double up.
The key in all of this is knowing your Mzone, and your opponents...
Hope that helped...