switching from mediums to deeps

That sounds like a good plan. Better Bee sells deep frames with "better comb". This is synthetic drawn out wax that I am told is readily accepted by the queen. I think it is somewhat pricey but you may only need 2 or 3 center frames to get the queen going next Spring, in the deep box. Or, you could put some drawn medium frames in the center of the deep to start with. They will build more comb on the bottom of the medium frames but in time you could cycle them out. Obviously you will need to feed to get wax drawn out in the additional new deep frames. Hope this helps.

Like you I ran all medium box hives for awhile. The main reason for myself to use a deep is that I also grow out colonies in nuc stacks and needed the ability to interchange the two systems. My production hive brood boxes now consist of two mediums and a deep. Though it could be in any order, I prefer the stack to be medium, deep, then medium. This way the bottom medium in fall is practically all pollen and serves the same purpose as a slatted rack for winter and early spring creating a thermal layer. Reversal prior to tossing on supers is simply rotating the mediums.

Introduce the deep prior to dandelion bloom and ensure the frames have plenty of wax. They'll draw it out in little time. Probably will only need the typical frame shuffle to encourage and ensure all frames are drawn evenly. Conduct the reversal when 70% drawn. Maybe during apple bloom.