I'll assume you've already tried cleaning and lubricating; since the chamber's rough yes, I'd polish it, (even if you cleaned it, it's possible the chamber is just fouled) I'd start with (Car) rubbing compound first since it's easy to remove too much metal and, then what ...I'd get a bore brush, a cleaning patch, and a drill. Put some rubbing compound, or metal polish like Flitz or Mecguiers on the patch, place it over the bore brush then attach that to the drill. I'd spin the drill inside the chamber for 5 or 10 seconds at a time then try a shell in the chamber (or however else you determined the chamber was rough). Once the chamber looks & feels smooth, I'd stop polishing right there, if the polish doesn't clean it up I'm not sure I'd progress to sandpaper but if I did, I'd use emery cloth, 1000 grit or finer, and i'd do it "wet" (with oil or break free) since that will leave a smoother finish then if the emery cloth is dry.
If the chamber isn't smooth a minute or two of polishing time, I think I'd stop. But I'd think the polishing ought to clean up the rough chamber just fine.
Since you can feel grittiness from the slide I'd try to ascertain what is causing that too. In your gun the weakest part is the action spring (the spring that fits over the barrel) so that's what I'd examine first. You may just need a new spring. Also it might just be on backwards (one end of the spring might be designed to be more narrow then the other and all you might really need to do is swap ends.) Or the spring might have flat spots/it became oval-shaped rather then round (maybe the spring got stepped on while it was removed from the gun).
If the spring isn't the problem, then have a good hard look at the slide and frame rails. The rails on the frame in your gun are relatively short, so I'd be surprised if that's where the problem is. If the rails were damaged you'd probably see it easily. And the slide and the frame are castings, or forged, and so it's not likely those have warped. In this style of gun most of the metal-to-metal contact happens between the action spring; the barrel exterior surface; and inside of the big hole in the slide where the barrel comes through. While you have the spring off I'd put the slide back on without it just to see how much grittiness you can feel then. Examine inside the slide anywhere there is or might be metal-to-metal happening, plus the hole at the end of the slide where the barrel comes through (might be a burr inside it but from what you mentioned about the slide binding half way back, this isn't likely). Also check & feel the outside of the barrel (perhaps chipped, burred somewhere, or just very rough, but if this were the problem it would be visible to you).
If none of this shows up the problem area, I'd get hold of some inside & outside micrometers and try to measure the contact areas of frame and the slide...then polish the rails, or wherever it is actually binding. But I'd start with 1000 grit, or finer emery cloth and sand it wet. 20-30 seconds at a time then try the slide again until you've isolated the problem area(s).