Well griffin, this is an all to common problem with bringing an old bike back to life. The issues to cause this can be numerous but you've already started to narrow it down
Compression is good and even on both cylinders and if it's backfiring than there is some sort of spark.
Check to see if there is good consistant spark on the missing cylinder, if not my guess is the points need to be cleaned on that cylinder and adjusted.
If you've got good spark, than take the carb off and give it a good cleaning. Check to make sure that every jet is open and that the float needle functions properly.
Now, with a good carb and spark and compression, it should work
Those are the usual suspects but I did work on a 360T once that had a bad coil that would cause the same thing intermittently.
Matt.