Wrong heads for a 273

I just got the deal of the century on a 273 short block that came with a full gasket set. Really nice gentleman had it and gave me a tour of his shop after we loaded in my truck. It is/was the backup block for his streamliner dragster that has been restored and won't be racing anymore. Here is a link to that story, I thought many would find it interesting.
The Silver Bullet Dragster Comes Full Circle
In his shop along with some metal fab equipment, he had three front engine dragsters, two vintage SCCA type cars, Bonneville salt flats car, a 33-ish Ford hot rod, and all manner of other gas powered toys in there. It was a lot of fun talking to him.

So now I have a '65 273 block that has high compression pistons (I think) and seems to be thirty over because I measure 3.655" with calipers. Bores are a bit rusty but will clean up I think. He kept it oiled somewhat but it was not fully protected from the elements over the years. I have access to a set of heads 587 heads and intake from a 73 340 that I'm thinking of dropping on. I know that they are considered on the large size for a 273 but the 1.88 valves aren't all that much bigger and I'm thinking they might help it breath at higher rpm and let it sing. Thought I'd rub on the bowls a little and need to figure out how much I can shave the heads (with those pistons) to reduce the chamber size and keep compression. Just got it home and need to get it cleaned up but there are other projects in the way. For all I know at this point, it could be locked up, but I doubt it. Just kind of talking out loud and looking for some feedback.

I'm gong to try to keep this build low dollar. I'm not even sure what I'm going to do with it yet. Maybe I'll stick in my 73 Cuda for giggles. Might have to buy a car to put it in. Maybe a 67 Barracuda convertible, I like silver to match the other one...