Myself, I'd use the VFD for one very important reason: Compressors normally are setup on a pressure switch and run unattended. And you have to think through the possible failure modes.
Sometimes you are at the other end of the shop when they start, sometimes you are up on the roof with a nailer placing new shingles, or in bed. Or miles away.
When the motor fails to start, and Murphy's Law says sooner or later it will... You probably can't get there fast enough to kill the power. And electrolytic caps go off like fireworks when they go - a Party Popper with tons of foil chaff confetti and some power behind it, with perhaps a flaming oil chaser on the old ones.
The VFD is smart enough to fault and stop, hopefully before anything blows up.
A homemade phase converter, not so much... The breaker might trip out before the fire reaches self-sustaining levels, but I wouldn't bet on it - remember, the breaker has to be heavy enough to hold Locked Rotor Amps during a normal start cycle without a false trip, so the motor has to stay stalled and drawing LRA current for a while to trip.
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