How does he lean if his ribs are pushed out and his nose is to the center? I have not seen this happen and really do not know how a horse could even do that.
Is there anyway to post a video of what he is doing.
Is there any reason that he is rushing through the corner because he has decided there is a scary woolie booger there?
If that is the case, I would roll him back against the fence and change directions just past the corner. I would do it as many times as it takes to get him to slow down. Then, when he is thoroughly sick of folding up and reversing, let him stand and rest in that corner.
Every time you are through riding, do some more of these exercises, stand him there for at least five minutes of rest (do it by your watch) and then, when he is absolutely quiet and settled (preferable resting a hind foot), dismount, loosen your girth and lead him back to the barn.
End every ride with a rest time and dismount in the corner he hates. I have never seen this method fail for getting any horse over hating a certain area, jump or place.
Every roping horse should end each ride by resting in the roping box (especially heading horses). Every jumper should end each ride by resting alongside of a jump it is Leary of. Every barrel horse should end each ride resting at a barrel and be led from the ring. Every lesson in a ring should end with each student resting their horse in the farthest corner of the ring, dismounting, loosening the girth and leading the horse out. If there is more than one student, they should end their rides one at a time and leave the ring one at a time. There should NEVER be a mass exodus to the gate. This would end a myriad of problems