I find there is often a low-tech solution to a high-tech problem. In December, I was the volunteer microscope instructor at a local museum. Sometimes I had a crowd of people around my table and I needed a quick way to put samples under the microscope without having to mount them on a slide, like human hair. So I experimented with a petri dish, as that is a quick way on which to dump samples. I found that the mechanical stage on my AO Series 10 would snap shut and therefore not work with anything but a slide.
Then the idea came, why not attach a slide to the underside of a petri dish? I experimented with the different petri dishes that I bought off ebay and found that a 90mm diameter plastic one from online science mall worked best. The diamter is about the width of a 3 inch slide. I attached the slide to the top of the dish, rather than the bottom, because the top is shallow and allows me to rotate objectives without hitting into the side of the dish. And the low-tech way to attach is Poster Putty (there are other variations of this temporary sticky mount) sold in any office supply store, maybe elsewhere too. Teachers, and kids, use it to attach posters, notes whatever, and it is easily removed.
I have taken a photo of this grand invention and have included a link below. The slide is held on the stage and it allows me to maneuver the dish up and down. Maybe it's not exactly what you are looking for, especially since rotating requires unsticking and sticking the slide, but until you locate this rare mechanical stage, it could do the trick.