Regarding the belt-- if you find that the belt you have doesn't handle the load of the compressor, the 4L300 you have is the same width and length as an A28 (which has a much higher horsepower rating). 4L-series belts are fractional horsepower rated and A-series belts are made to transfer quite a bit more power. I've got no idea what an A/C compressor draws, but if you need more, a suitable replacement is readily available.
Any industrial supply store (Grainger, et al) carries A-series belts for industrial fan, etc. applications. I see that you have a "green" belt, which is the Gates brand lawn and garden 4L belt, if I'm not mistaken. As an aside, I greatly prefer Gates brand belts to anything else. I've found that a Gates 4L-series belt will handle as much power as a Browning A-series belt.
Looking good on the project!