he must maintain a Patronus strong enough to keep them hidden from Dementors but not so strong that it starts destroying Dementors or attracting attention.

Quirrell may not understand in detail how Harry's Patronus works. So from his perspective, it just indicates that Harry understands and controls the charm really well. So this isn't an unreasonable assumption on his part. Still, it would make sense to try to get more information before trying.