As noted, media blasting is not going to give you a machined surface. At best, depending on the grit used, it might give a fine satin like surface. The other issue with media blasting is that it will not be effective at removing the chrome finish.
'Chrome' (actually layers of nickel with chrome on top) is very hard. Anything that abrades the nickel is going to tear through the aluminum pretty quickly. With the correct media, you can remove the top chrome finish; but, not the underlying nickel layers. The media blasting may etch the nickel enough to allow a powder coating (or paint finish) to attach successfully. I would not use a clear powder coat because there will be a difference between the color of the bare aluminum and the abraded residual nickel surfaces. Depending on what you used as the media there will also likely be a texture difference between the bare aluminum and the nickel areas because the aluminum is so much softer.
There are chemical treatments that can etch the nickel taking everything down to bare aluminum. These are very nasty chemicals and you would likely have to find an electroplating shop with the facilities to carry it out. Once this has been carried out you would have to take the wheel to a wheel shop to have it micro machined to restore the machined surface. Then you would need to have it recoated with a clear finish of some sort. I sense that this is likely to be $$$$ by the time you are finished. If you have a real taste for expensive, rather than finishing with a clear you could then send it back to the electroplater and have it re chromed. With good workmanship the wheel would look very close to OEM and probably cost twice as much as OEM. Then you could wait for the chrome to start the peeling process again.
You can micro machine the face surfaces of the wheel to remove the chrome and restore the face surface. This would still leave you with chrome on the surfaces between the spokes. I don't know how you would get rid of that without resorting to chemical stripping.
I have the 2000 factory 16/17 wheels with the machined clear coated finish. On the right rear, the previous owner left it with two small scrubs on the rim lip and the clear coat lifted in three spots allowing surface corrosion. Repairing the scrubs, micro machining the wheel and refinishing with clear including dismount, mount and rebalancing was going to be the equivalent of approximately $600 US per wheel.
I think your lowest cost solution will be to abrasive blast the wheels to remove the loose chrome finish and abrade the nickel finish enough to allow a top coat to attach. I would select a solid color finish. You would need to do some research as to whether the appropriate paint or powder coat is more durable.
Any finish that deviates from the OEM finish will devalue the car for a buyer who is specifically seeking an unmolested original car. However, a refinished painted / powder coated wheel may have increased value compared to a peeling chrome wheel for a buyer that is looking for a 'nice' NSX.