My technique has evolved over the years, currently I use only BSI thin CA and open cell foam as the applicator. I find that I get about 0.002" additional diameter with each coat. I turn the to about 0.006" less than desired final diameter, then apply 4-5 coats. I try to use accelerator sparingly and try not to apply until the coat is nearly cured -- usually no accelerator for the first two coats and then with accelerator between the final few (I use BSI accelerator in spray bottle, not aerosol). I then use a sharp skew to turn back down to about 0.001 over final diameter. There is usually enough material that I can get the barrel perfectly cylindrical with all of pits/valleys removed. Then I wet sand with 3M wet/dry paper 800-1500-3000. Then check to make sure I didn't sand through, its not the end of the world if I do but it saves a lot of time to check at this point vs after the MM. I will usually just apply additional CA if I sand through, but it can cause different colors in the wood which is sometimes noticeable, so I do try my best to not sand through. Then I go through the MM pads, cleaning the blank between each pad. Finish with HUT ultrashine and then apply renaissance wax after assembly. I think I can get a respectable finish, but I know others do a lot better. At some point I will graduate to buffing wheels, but for now this seems to work OK.
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I find that temperature, humidity, age/type of CA, age of MM pads (or debris), and "roundness" (for lack of a better term) of the blank play significant roles. I also find that some materials will tend to have slight valleys and/or pits and application of CA can make this worse. If you go right into sanding the slurry can make these even worse, which causes sanding through prior to removing all of the pits/valleys. If you use a skew to make sure the finished blank is perfectly round before sanding it reduces the amount of sanding and helps to prevent sanding through.