Splitting the cases means taking a lot of things off the outside and then a lot of things out of the inside... and remembering how they go back. Depends on how much you value polished cases. I think tearing down to bare cases and covers then having them soda or vapor blasted would be the best way, if you're going through disassembly/reassembly then having them cleaned up well with blasting before trying to polish them would make a lot of sense to me.
Even very fine abrasive media in a sandblaster will give a good base finish but I haven't ever polished them, I put "GunKote" on a few engines some decades ago and wanted a clean surface for that. BTW, that stuff is great.
In my limited experience, polishing does not have many shortcuts. A strong arm and a case of beer plus a lot of time...
I have a polishing lathe but that's only good for relatively flat things. A cloth disc on a drill will float around corners and get into the fins a bit. More aggressive compounds will round off sharp corners fairly fast with power tools.
In general, polishing tends to be a rabbit hole you go down and never come out of. There is always some difficult to get at stuff that just needs "a little more work". By the time you finish the last part, you'll see flaws in your first ones and start over to give them a "touch up"... and repeat this a few times. Finally you'll realize that the aluminum alloy just will not hold a polish, and that a polished surface won't hold a coating.