Well that's an interesting question and it may call for an unconventional answer.
You could purchase an air bottle (similar to a scuba tank, or actually an old scuba tank) like the rock crawler folks use. They use these to air up tires in the middle of nowhere or to run air tools etc.
These are very strong air bottles that handle a lot of high pressure air. You'd need a regulator of course.
You wouldn't want to waste the high pressure, so you'd want to use your air compressor to put air into the tire (that your compressor could reasonably handle) and then top off the tire from the bottle.
That's one possibility and certainly a unique possibility.
Good luck.