The issue of single and 3 phase electrics always draws interesting comments ! The fact is that single phase has been with us and been used by many for decades, that it has a capacitor or a centrifugal switch, and may vibrate is true but it is also simple technically. When I bought my Myford S7 in 1971 I knew nothing of all of this, it had a 1Ph motor – it just worked and has continued to do so for over 50 years. The lathe and drill have lived in a damp shed for the last 40 years without issue. Time passed and when I needed 3 Ph I built a diesel generator, there is no 3Ph in my area and I needed 17Kw for one machine and 11Kw for the other.
Static converters are not cheap and rotary ones even dearer. In the main their plug and play, no need to find star point Etc or convert to 220v. They will run multiple motors with simple adjustments to the control. The steinmetz circuits are fine and work if you understand how to do it.
Then there’s the VFD – Cheaper than converters but mostly need 220v motors and may need extra work to make them comply with some regs, technically complex and whilst very clever, to get the best out of them one needs to understand how to set them up. Variable speed is a big bonus. How well would a cheap one stand up to a damp shed, never mind salt air.
It comes down to what you’ve got, what you need, how much you understand electrics and how much money you can spend.
That single phase motors are cheap because they suck, I beg to differ !
As to the original question, change to delta, run a steinmetz circuit, Buy a cheap VFD or find a single phase motor of 1/2 or 3/4Hp. I fancy that there will not be much cost advantage to any of the options.
Good luck and best wishes. Noel.