Adam you don’t really quantify whether the mess or flattening is the main issue. There is some mess with all methods. As for flattening this is minimized by rotation of the stone and using the whole surface.
Once the primary bevel is established sharpening is very quick and even just using the strop brings back an edge for some time.
As for flattening I use a CBN plate. Very quick and you can see your progress very clearly. Splash with a running tap, the vacuum holds them together, rotate, slide some more, flush and you are done. Far from constant, just periodic. The price of CBN plates seems to have come down considerably.
Think about your ratio of work to sharpening, perhaps something is wrong with your sharpening results? It could be an easier fix than replacing your whole system.
You can do a lot with very little! You can do a little more with a lot!