In theory, Kodachrome can be reversed. In practice, however, I'm not sure it's a very good idea. These are expired films. Even though Kodachrome was discontinued not that long ago, what's usually found on the market are very old rolls - often from the 1970s and 1980s, extremely rarely post-2000, and then at unrealistic prices. To be honest, with the ones I've tried, there has always been some level of fogging - ranging from moderate to quite heavy.
If fog is present, reversal may not be a great idea, unless you manage to suppress it completely during the first development while at the same time preserving sufficiently high image density. The only approach I can think of is aggressive suppression with restrainers combined with heavy overexposure. The problem is that it's hard to run proper tests, and different batches of expired film will behave differently…
Regarding making a developing tank yourself - it looks like quite a hassle. If you already have a printed roll and the design files for the tank itself, you can find a paid 3D-printing service near you. I've also seen some interesting DIY ideas - for example, making one from PVC pipe of a suitable diameter, with cut and flattened sheets made from the same pipe.
From time to time, old Soviet tanks for 8/16 mm film do turn up. All of them are quite awkward, bulky, and… easily breakable. I know, because I recently smashed mine
This time, though, I'm going to order a modern AGO reel for a Paterson tank.