You probably do not want a BLDC motor, but:
https://en.wikipedia.org/wiki/Reluctance_motorThese do not get much attention, maybe because they are not "fashionable" or maybe because the power density is lower.
They do have some inherent advantages for use in a turn table, and this is the same reason why they are also used in HDD's, and that is that they have 0 torque ripple, and that is in turn because they do not have permanent magnets.
Did you also change the title of this thread?
I responded earlier, but had not noticed then it was for a record player.
There is nothing special about a motor with 120 coils, They are still just 3 phase motors, with a number of inductors in series or parallel, (or combinations of that).
I also am in doubt if it would be useful to cram in as many inductors as you can.
High mass of the rotor, combined with low low friction are probably at least as important.
After spin up, the motor itself only has to deliver enough torque to overcome friction losses and prevent rpm from decreasing.
With the right motor geometry, it can be driven by a perfect 3-phase sine wave. If the motor geometry is not perfect, then it can be compensated for by pre-distorting the 3-phase sine waves as part of the FOC algorithm.
Have you considered air bearings?
"applied science" has a nice ecplanation, and I think even a tutorial for making them: