Heads up, Large blinds strategy

Hey everyone. I am a long time lurker to the forums with only two posts under my belt so I apologize in advance if this has been discussed in detail before. My question concerns general strategy when heads up with an opponent towards the ends of an SNG (in this case at party poker) with fairly equal stacks of ~4k and blinds 150/300 up to 300/600. At what point does the name of the game become "push and pray" preflop? I find around the time the blinds become 200/400, there is no room left for fancy play (expect maybe to limp with a big hand to trap your opponent).

With the blinds this high, what is the most efficient strategy in terms of deciding what hands to push with when you have the button and what hands to call your opponent's push when you are sitting on that massive big blind? I think I tend to steal too often and find myself running into hands that dominate mine or are a 2 to 1 favorite. I also understand fold equity changes for each opponent you play, but does anyone here have some sort of guideline of what hands to hold'em and which to fold'em when finishing an SNG under such conditions?

(BTW, this pertains mainly to the $10+1 and $20+2 SNG's as those are the only ones I am currently playing)

[Xenod]

When it starts turning into an all-out push-fest any Ace becomes your friend, as does most pocket pairs (44 and up). You can also get aggressive with any 2 high cards.