I think quirrel is Harry from the future. Harry decided not to mess with time until he's older, but maybe once he's older he realized that he can break the time travel restriction rules and travel years into the past. This could possibly explain why quirrel knows so much about Harry. It also explains their magic interaction possibly. This would also explain how quirrel is so rational, whereas it would be surprising that Harry would randomly run into someone as rational as himself in the small number of people he's met in the wizarding world. Quirrel could've even been the one who gave petunia the potion, thereby using that one difference (Harry traveling back in time) to explain multiple differences between hp and hpmor.
Any thoughts on my theory are welcome, I'm curious if this is a commonly held belief. Maybe the source of magic showed Harry a way to perform time travel that could exceed the (6 hour?) duration.