I do very nearly as you. I use a paper towel to spread polishing compounds onto the cue and then slow the lathe down to around 60 or 70 rpm and using a variable speed auto polisher with different 7 inch pads for different compounds, I polish the cue. Before using each pad I put the pad in a bucket of water and then wring out. I want to keep the friction at a minimum so that I don't burn the finish. I then run the buffer at around 16 - 1800 rpm with the outer edge of the pad just barely on the cue. What I am trying to do is have the pad buff lengthwise on the cue instead of cross grain. In this way I don't get the polishing rings around the cue normally associated with polishing on a lathe. I used the 3-M Imperial hand glaze as a last polish for years but was told that the Ultra Fina was supposed to be a better shine. I know it sure costs more. I may have to try it again.
One thing I have learned is it is false economy buying cheap sand paper. All it does is cause much more work trying to eliminate scratches and swirls. Paper is only as fine as the coarsest piece of grit on the paper. So often while wet sanding you get the finish nice but there are a few scratches left that don't want to come out and they are caused by the sand paper that you are using. I used to shop around trying to find the best price on paper but I no longer do this. I am now paying over 2.00 a sheet for finishing paper, from 1000 through 3000 but it is well worth it in quality and ease of getting a good finish.
Dick