Bad hinges, the hole for the pin is wallowed out, will make the door move up and down, in and out so when you put a bushing in you lose the play. Check the play before any adjustment.
Also make sure there are no cracks in the striker area.
Make sure the door clasp centers on the striker so when it latches it does not lift up or push the door down. Then sneak up on the door closing tight.
So sorry I didn't see this. Let me go back and read it all and get caught up. I feel turrrible (Charles Barkley voice). Quick answer is you can remove the ws and reinstall them with no problem and no added glue. Done it many times....lol. More glue certainly doesn't hurt but it's not necessary. As far as the corner....You have to sorta pack the corner by barely seating the first few inches of the top rail and mash it back toward the corner until it doesn't have that bounce out.
Gimme a while to read all of this.
Just for future reference and maybe to help anyone else out, back in the first part of this thread you will see some info I posted about door hinge bushings. Most door fit problems ultimately come back to hinge bushings. If you open your door and grab the bottom and lift up and you have any slack, you need to address this. All other adjustments are difficult or impossible if these bushings are bad. Replacing weather stripping with the DC product shouldn't change your door opening or closing. All you may have to do is slightly adjust the striker.