Well, YES, NO, and SORT-OF???
Your refrigerant evacuating and and recharging skills might be helpful, however, you cannot capture the R-134A refrigerant using the same equipment that you use on refrigerators unless you have empty refrigerant tanks to use. The refrigerants are not compatible with each other.
Then, yes, it is possible that your A/C clutch is slipping. You can verify this by listening to the sound of the compressor. You can usually hear the clutch making a grinding sound. There will usually also be a bunch of rusty-looking dust around the area of the clutch due to the metal tearing off of the clutch surfaces.
Then you need to decide if you want to replace the clutch assembly or the entire compressor. If the clutch assembly is all you need, then it can be replaced without any type of refrigerant recovery needed. It is also a whole lot cheaper to replace than the compressor (see picture and link below).
However, the clutch can be pretty tough to replace without the special tools needed - especially if you have never done one before.
Clutch listing for AC clutch at AutoZone
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