The flourescents will have a capacitor too but I don’t think it would be up to the job.You want something more like you find on a motor, and it want to be continuously rated too.
If you set the three phase motor up to run on single phase, you will get , in theory, about 2/3 of the power. Practically, what you will get is in my experience more than enough. I have an 18 inch shaper, one setup that I have tried with that limited it to a quarter of the nominal horsepower, eg 3/4 hp out of a 3 hp motor. You would be surprised how big a cut you could still take. I more usually run that machine with a single phase set up, without the starting capacitor. This means giving the pulley a suitable kick at the right moment. Running like that, eg nominally about 2/3 of the original power, it has taken a cut of 0.250 thou across a piece of cast iron bar. So lack of power is not usually a problem.
regards
John