Being a former swimmer myself, you will literally die trying to swim a 500 breaststroke. It's by far the most physically demanding stroke out of all of them. While I'm biased towards it, it works more muscles at once than any other stroke. If you're going for a fast time, you will tire extremely quick.
Freestyle is by far the fastest for long distance. You don't need perfect technique for it, while in breaststroke you do.
Edit: I don't even know what the PAST is, I imagine it's some sort of swim qual. But in my water polo days we'd swim around 1000-1500 yards a night, then get out of the pool for 120 push ups. Most of the strain should be on your core, back, and shoulders from swimming. In my experience doing those push ups after a swim set was no harder than doing them before a swim set.