I think it's time to bite the bullet and build a worm drive... If there was a better gearing way to do it they would be available that way...I's just the smallest package high reduction gearing design available.
I've cut many a spur gear and angled spur gear...so my first thought was build spur gears with 45 degree angled teeth so then the shafts are at 90 degree. But it's just not as nice as a worm drive for a small footprint high reduction gear set.
Since you're gonna cut a lathe spur gear the big gear should be the easy part for you (and me) . basically an angled spur gear with the center of the tooth dished.....the worm is the part that has been intimidating me.
There is an article in HSM about fitting a worm drive to a mini lathe mounted indexer. The worm was to drive a module 1 gear - 20deg. pressure angle and tooth spacing approximately 1/8 inch. The lathe tool was ground to a 40deg angle instead of 60, and the threads cut at 8-TPI. The angle and TPI would have to be changed to match whatever gear you choose. While the best way to transmit power between a worm and a spur gear is to angle the worm shaft so that the faces are mostly parallel, a straight on drive will work for the small amounts of power involved.
The higher the ratio, the more tolerant the indexer is to hole place jitter. 40:1 for most indexers, but 90:1 for most rotary tables. If I was to do an indexer (and I probably will later this year), I would do 40:1.
I have a rotary table that was made ( where else ) in China and I know it is not 40:1. They make a kit consisting of plates and crank and fingers to replace the hand wheel and convert it to a dividing head. Now since they are NOT using a 40:1 ratio, this was what convinced me that as long as you design the hole plates to work with the ratio you have , it doesn't really matter what the ratio is to a point.
I am looking at using 30:1 as it is what is available.
I have one of those Chinese tables, too. It is 36:1. 10deg. per turn of the handle. The bearings are bad, the backlash ridiculous, and the center recess not in the center. I don't use it. I keep it as a monument to my unwise thriftiness.
Looking forward to the project.
Larry