=================================== Your plane looks very nice. My only problem would be that it is too pretty to use.
Actually a mill is ideal for jeweling, as you can precisely space the swirl marks. You should be able to get a mirror finish using only the tools you have. Try some of the ultra fine abrasive paper available at many automotive paint stores. Be sure to wrap it around a flat support such as a hss lathe tool blank. I have several 3/4 blanks just for this. An alternative is to use your mill table as a surface plate and put the ultra fine paper on this and lap the frame plates.
From what I could tell from the pictures, your current finish is more than adequate as a base for engine turning.
Brownell's sells a kit for bolt jeweling that should be just the right size for your plane frames.
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More than likely you will want to apply an urethane or epoxy clear coat to protect the finish.
If you want to simulate actual "engine turning" where the metal is "machined" you may be able to do rosettes by grinding a chisel shape on a hss rod and "nicking" the end with the desired spacing.
Unka' George [George McDuffee] ............................... On Theory: Delight at having understood a very abstract and obscure system leads most people to believe in the truth of what it demonstrates.
G. C. Lichtenberg (1742-99), German physicist, philosopher. Aphorisms "Notebook J," aph. 77 (written 1765-99; tr. by R. J. Hollingdale, 1990).