No first-hand knowledge here, but I'd guess that the alcohol in the FP would partially dissolve the alcohol based stain, picking up color from the sides/back as you polished. Seems that the first step in your scenario should be a spray coat, lightly applied, that would seal in the stain. Then polish as usual.
As always, a test run will teach you volumes...practice on some scrap till you've got a usable technique.
Good luck,
Steve
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From Nacogdoches...the oldest town in Texas.
http://www.stephenkinnaird.com