Well, I'm sure you wont like to hear this but: No way! If you want to do a propper polishing you need to unlace the wheels. As I too have struggled with polishing in the past, I'd like to recomend using "sanding stars" instead of sandpaper. These cost a little but they pay off! I have two sets of 180-240-400-600-800 grain and they are much quicker, less abrasive and give a better surface than sanding by hand. Plus, they last quite some time.
After you made the last sanding step (800), the number of steps obviously depending on the condition of the parts, let it sit for about 15-20h before polishing, to give it some time to build up a thin oxide layer. The polishing itself should be done with a fast running and strong disk, so you can create enough heat on the surface. This will "melt" it to a chrome like shine.
Don't use polishing fuids! These are just fine sanding agents but not polishing - they'll do the opposite and the surface is very prone of getting dull even faster. If not, it's just the wax of the so called polish that prevents it for some time. A good polish needs heat.
That's just some advise that I got from a guy who does this as a professional and I have to admit, on porous castings, as you might have on the bike, it's almost impossible to "seal" everything up to a state, where corrosion (dullness) doesn't get in.
Oh, if you throw out the old conrods - can I have them?
Good luck buffing up the beast!
Andreas