If using a standard commercial worm gearbox, I'd size it appropriately for the job at hand. Probably for a 24" diameter workpiece, I'd want a worm gear maybe 8" diameter at the minimum, which would be 5 diametral pitch, 40 teeth, and the reduction would be 40:1 This will give you a max of 62 rpm with a 2500 rpm motor.
Having looked inside of some cheap rotary tables, I'm not all that impressed with what they give you. The worm is typically not in an oil bath, and is not supported on both ends. However, the worm backlash is compensated for on an adjustable eccentric, although this may involve some fudging to get it really tight as usually there is some means to stop it from going in too tightly from factory.
The cheap rotary table also has very limited end thrust capability on the worm shaft....ie., "they don't got real bearings in 'em "
So because they use crude plain bearings (ie, a shoulder on the shaft rubbing against the base metal of the adjuster housing), they can wear themselves loose.
Many commercial powertrain gearboxes have a worm shaft that has the worm thread integral with the shaft, meaning you cannot take the worm off the shaft, because it is the shaft. And, reboring the housing to make an eccentric adjustable worm would be quite a trick since the original casting was not designed with that intent. You need some room to work, to make an eccentric worm adjuster.
I would then resign myself to the purchase of two hardened worms and a matching bronze worm gear from Browning Gear, or Boston gear, wherever. Then, I would build my own gearbox. I have a machine shop, so this is practical for me.
Instead of making an eccentric worm housing, I would instead mount the two worms end to end on the worm shaft. It would take some work to face the worms off so that when placed on the keyed shaft, the helix lines up properly. Then, backlash adjustment would involve placing a precision thin shim between the two worms, in effect, seperating them, and taking up the lost motion in this manner. Trial and error would determine if the worm gear is accurately made so that there are no places in rotation where it all binds up tight...too tight. Then, the whole mess: bearings, worms, spacer would be sandwiched tightly together on a shaft with no endplay whatsoever.
I'm not saying that this is the only method, or that you might be able to make do with less perfection, but it may give you some ideas on what to do, and how to approach it.