With an above-average chipstack, I'm playing the same solid game that got me to this point, trying to slowly add chips to my stack. I rarely feel the need to vary my approach at this phase.
I will continue to play this way until I am either at 50% of the average in chips, or I am the short-stack in the field. Once this happens, I am generally looking for a hand to push hard, in the hopes of getting a caller and doubling up.
As I approach the bubble, I look for the players that seem to be willing to give up their blinds to avoid a confrontation. Generally, there will be one or two who seem to be keeping their head down, trying to hold onto enough chips that they can most likely back into the cash.
A lot of players will blatantly steal the blinds with any 2 cards here, but I prefer to only raise with decent cards in later positions. Ideally, I never want to be thinking "please don't call me" when I decide to put in chips. Cards that can stand up to a reasonable calling hand or a small reraise are what I am looking for, and I'm making the same "standard raise" that I have been using the entire time (in the range of 2.5BB to the size of the pot) no matter what I choose to come in with.
Once we are in the money, I will generally sit back and let the first few people take each other out unless I get a premium hand. This is a good time for me to identify the people at my table that I will be challenging, and start observing their play, since they are new to me after the seat draw.
Short stacks are looking to mix it up with anyone and double-up, so I don't like to give them the chance to. I have to have a rock-solid holding to even steal their blinds.
Unless I am close in chip count to them, I also stay away from challenging the big stacks at the table. There is no point in taking a coin-flip against someone that is willing to risk 8% of their lead to take you out.
Usually, the players that I will go up against are the ones that have slightly more chips than I do. It is very unlikely that they will put many chips in against me with less than a premium hand, because they know that by doing so they could drop below me in the payout. They can "make money by folding" if I go out before the shorter stacks do, so I try to give them the opportunity to do that.
Hope that helps - congrats on the finish, and good luck on the next one.