One further comment on poly - - -
The usual practice with a CA finish is to apply many thin coats, and then sand/buff after it has cured. It's possible to do the same think with poly - in fact, if you are using wipe-on poly, you pretty much have to do that because the poly contains a lot of solvent.
But there is another approach with poly that you may want to try - sometimes called 'rotisserie finishing'. In this approach, rather than using commercial wipe-on poly (or regular poly with additional solvent), you apply heavy coats of regular unthinned polyurethane - with a brush. This is normally done with solvent-based poly, but I have done it with water-based material. Leave the piece rotating on the lathe running at its lowest possible speed (ideally, 20-40 r/min) for at least an hour or until the poly 'sets up'. Allow it to cure fully (probably overnight), and then repeat the process. The person who taught this method to me recommended four heavy coats of poly. Then, after the poly has fully cured, sand through the grits (being careful to not sand through the poly) and buff.
The trick in this approach is the heavy application of poly combined with the continuous rotation. If you just left is stationary, you would get drips and runs - disaster - but because the piece continues to rotate as the poly cures, it self-levels.