Update:
Just bottled a few more bottles of beer. This time with the bottles at 32 degrees, and the beer at 32 degrees, and the beer gun at 0 degrees F (it was in the freezer).
Also the beer was pushed at 2 psi.
Guess what? Problem solved! Works like a charm.
Yes, it spells most of this out on the last page of the directions. If I would have read the entire manual.