Sorry to hear that Tippy is having such trouble.
The thing about abscesses if they haven't ruptured on their own, is that they often need to be manually ruptured and flushed, and then the cat placed on antibiotics to get them to heal. Some will rupture on their own, but there is no way to know for sure. The longer they remain, the greater the risk for permanent damage or starvation.
If you are absolutely unable to get him into a carrier for a trip to your vet, you have a few options:
You can ask your veterinarian for a sedative that you can give him in order to get him there. Since it sounds like he will need to be sedated in order to have the abscess treated, this may be the best bet.
You can purchase or borrow a live animal trap and place it in the garage to trap him for the same purpose.
Depending on your local ordnances, you can sometimes get Animal Control to come by to trap him for you.
If you don't get him in, it is possible that it will rupture and heal on its own, but with it being on the face, I wouldn't recommend taking the chance.
Hope that helps. Please let me know if you have any other questions.