prepping brushed finished cenerlines for polish/buff

I have a set of old school centerline auto drags and would like to polish them to a mirror/high luster finish. The issue is, the existing brushed finish is course enough to snag a fingernail, looks like 36 or 50 grit finish. How would I go about sanding these smooth enough to polish/buff without gouging in spots?? And how to get in between the rivets? I'm thinking something like a flap wheel or disc. I do have access to a large enough lathe to spin them while working them. 
T.I.A.-Jeff. 
Mods- move this if you wish, just figured it get more traffic here. 

I'd start with 320 wet & work my way to 2000 & polish

That's how I do factory wheels with machine marks when I polish them