Someone could do a power quality analysis. Some UPS systems are frequency sensitive, but the compressor has me slightly baffled.
A couple of thing to look at:
Turn the AC off. Go on generator power. Wait 5 minutes. Turn on AC. Does the AC start within 10 minutes?
I'd make sure that guidelines for the install of compressor heaters and hard-start kits are followed.
I'd add a hard start kit. Here is one for 5 ton.
Hard Start Kit,5.0 Ton A/C Units {Dayton 1BAF1}[1BAF1]
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Check the grounds. Although this should be more of a heating issue.