[Brian]

On the cheap? Can't you find the correct bearings?
A while back, I built a 255 cube 21 stud....I used a 37 block like you've got, first operation was to ultrasonic check all cylinders to ensure sufficient 'meat' after a rebore to 3 3/16". The machinist assured me there was adequate thickness to allow yet another .020" bigger again. I used a Scat 4" stroke crankshaft for a 221, another story in itself to make that work, and got Ross to make me custom flatop stroker pistons @ 3 3/16" dia. Bores were finished to correct size incorporating torque plates as recommended by Ross.
Recently had the heads off....the rh bank, all combustion chambers were oily, lh side exhibited just normal carbon deposits. All cylinders, particularly rh bank were scored. #7 piston particularly, could be rocked a lot! Pulled engine to bits....all pistons and cyl walls were scuffed/scored. Again, measured everything. The pistons had .0045 clearance. The scoring was not as a result off insufficient clearance of the forged slugs. If you look into the water jackets of a flattie, you'll observe that the cylinder walls step up in thickness about 1 1/4 below the deck. Well, the afore mentioned #7 cylinder had a crack that followed that step.
I believe, that boring a 21 stud out too much allows cylinder walls to flex and distort, which led in my case to the above problems. Just because one can bore a 37-38 block out to 3 3/16, doesn't mean one should!!
If you want a Scat 4" crank to suit your block, let me know! I have one going cheap.