Sounds like it's time to make a decision. I have very little confidence in the stop leak product. It may get you through the summer though.
I chopped up a brand new can tapper this year to use with my gauge set. The truck needed a flush and fill after a compressor burnout and the Saturn blew the thermal fuse embedded inside the magnetic clutch. All of the can taps that had flare (acme) fittings on them were car size and wouldn't fit my home size gauge set. So I bought one of these:
I put access valve tubes just like the one in your unit on the ends of the hoses.
Now both halves connect right up to my gauge set.