I’ve converted two motors which were wired star only. One was a simple job, the other needed a little more care as the windings were well lacquered/varnished.
1 1/4HP motors do not seem to be used often. One of my motors was a Brook Crompton (I think) in that size. That one was the simple/easy conversion.
As another alternative, although more expensive perhaps, would be a 230V single phase to 415V three phase VFD.
Further alternatives are three phase converters, although the variable speed and other programmable options would not be available. I don’t particularly like them. I intend to stick with VFDs whenever possible.