[Brian]

I bored a 37 block out to 3 3/16", fitted a 4" stroke crankshaft. Sonic tested the walls before hand, had 0.145" wall thickness minimum after boring to that size. Got Ross to make me custom flat-top pistons to suit...followed their instructions to the t, including using torque plates for final sizing. Not a good engine; it always had lots of crankcase pressurisation, detonated terribly [had 165 lbs compression], so thought I'd change the heads to lower compression....that's when I discovered all cylinders and piston skirts were scored.
I have built many engines over the years, from stock to 284 cubes, and this one was a disaster!. Subsequent to that, I had numerous emails and phone calls from another guy whose 36 LB engine was bored to .080" and his cylinders scored too, running cast pistons. 36 LB engines have thin cyl walls; boring them to .060" can be risky....
Now, I have no proof, but my theory is just because you can bore a 21 stud to xxx oversize, you run the risk off having the cylinder walls flex in use, leading to distortion and the resultant scoring, on account of them losing a degree of structural integrity.
To Dave/Green Bay, 35 blocks have thin cylinder walls [same as 36 LB]. 37 blocks are somewhat thicker, and, as I discovered can still be problematic at such an oversize.
Seth, with your 37 block, a possibly safer option would be to sleeve the dodgy cylinders, alternatively, find another block.
My opinions/experience only, take it for what it's worth.