Bolt dimensions for Peloton cleat
All 3-bolt shoe plates are M5 (5mm by 0.8mm per thread). So are 2-bolt. That's the thread size insofar as the wider world is concerned. That's not really what you care about.
What you ideally want is a Look Delta cleat bolt that's the right length for your shoe. They are funny little bolts and can be hard to find in just the right length if the stock ones aren't working for reasons like you're encountering. But, you need them to be low-profile like the stock ones are.

If you are forced to improvise from the hardware store or from what most bike shops will have, the best you can probably do is M5 button head bolts with large diameter washers. The total stack will probably be thicker than proper Look or clone bolts, so they may poke out or come close to it.