I appreciate that it's slightly altering the PoD, but the best way to get around the noted problem of the Stanley brothers is to present them with a fait accompli. Obviously, Richard tried this in OTL,but didn't quite manage it.
One of the difficulties of discussing Bosworth is that it is woefully unrecorded. Best bet appears to be having Northumberland support Richard's mad dash across the battlefield, the added troops being enough to decide the day before Stanley arrives. If he could: it's clear that the terrain wasn't the best. However, if you're looking at writing a TL based on this, that dearth of contemporary accounts means making a change can't be immediately dismissed as implausible.
By this stage (Richard's charge), Norfolk is dead, so Percy is chief among the Ricardian commanders. If his cavalry can kill Henry, while his infantry rescue Norfolk's battle and rout Oxford, then it's a massive Percy win, although such is easier said than done.
He will be rewarded, and fairly handsomely, but nowhere near as much as Doosung suggests. For starters, if the Stanley forces are still intact, they lose nothing. Beyond that, others have already mentioned "over mighty subjects". Also, Richard had developed and nurtured his own northern network of patronage while Duke of Gloucester. He's not abandoning that wholesale. It's very likely that Percy becomes preeminent north off the Humber in the aftermath, but he won't become dominant. He might be rewarded with the Council of the North, but he might not be. It's a balance between gratitude and giving one man too much power.