polishing aluminum to mirror finish

[kling8]

I have these parts block of aluminum with 4 holes about 1.25" dia depth 2.0" then taperes cone shape down to .5" dia. 1.0" depth. It is a through hole. I'm having trouble getting the finish I'm after without spending a ton of time. Been trying few different compounds and cone buffers.

After a mirror finish?
Speeds feeds compounds type of material to buff with?

[JoeGranite]

Have you ever had these parts finished in a Vibratory machine?

How many parts do you make?

Giant Finishing - Made In America - Vibratory Deburring Equipment & Media