I think it should start your compressor. I also have a 7.5 hp compressor (with a true 7.5 hp/240v Marathon motor) . This is a big starting load on the generator for sure. But the 003 starts it with just change in pitch, moderate frequency sag and about two seconds of grey smoke before returning to speed. The % load meter reads close to 70% with just the compressor running after the initial start pegs the % load meter.
I also started my 5 ton air conditioner. It really bogged down for several seconds but it got it started and came back to speed. I did have some other small loads on the generator at the time (maybe 10-15%). After starting the a/c, the % load meter only read around 50%, even though it is fed with a 2 pole 50 amp breaker.
It may be something as simple as the wire size you were using or you frequency is off enough that the motor didn't like it. But it should definitely start your 7 1/2 hp motor with minimal complaining.
Good luck,
John
Edit: I did have other loads on the air compressor when I started it but they were minimal (<10%)