A junky platter is all that you'd need, or, even a kitchen-type Lazy Susan.
You can find the center point of a circle fairly easily. So, with a Lazy Susan-type rotational platform, you could drill in a center spindle (easy to make).
I mentioned Lenco TT's as having 16rpm capability; good luck finding an affordable Lenco anymore. I'd look to the 50-8, or 50-16 models, as they're not the ones that collectors and enthusiasts are after.
My first one was a BIC, or, other form of mass produced changer TT, that I extracted the bearing and platter from. i mounted them to a piece of plywood. I could clean the records, and tuck it away in the closet. Then I found out about the VPI vac. wand, and, things drastically changed.
Its worth whatever effort that you can put into it; and the rewards match the effort.
If DIY isn't your thing, there are lots of inexpensive options; and many more spendy ways to arrive at this same end.
