The seal is usually formed on the front face of the door not on the edge, installing a thicker/better seal for the face side would eliminate the need for the edge sealing.

Bryan, I would look at installing a 'tongue'/strike plate for that catch so the wood on the jamb doesn't get beat up any further.

Jason
M80 v2
VP160 v3
QS8 v2
PB13 Ultra
Denon 3808
Samsung 85" Q70