I have worked with all of the Stains and coverings, in those colors too. Four coats of PolyShades won't do you any good. Poly shades doesn't change color much after the second coat. The extra coats will only act like paint obscuring the grain. Not sure but the Bombay Mahogany would only be slightly muted, from the stain underneath. In otherwords I am not sure what you hope to gain by combining the two. BM is a very reddish color not like regular Red Mahogany Stain (see below) Mineral Spirits will only work if you immediately stain right behind the application, this acts as a temporary "sealer Coat". As an alternative, mix up a small amount of poly with mineral spirits about 50/50. wipe on with a rag. This was done as an experiment on my last project worked well. The Poly was thin enough that it was absorbed below the grain allowing for the stain to still do its "thing". My last project was done with Red Mahogany stain. Word of warning it is not "red" But red tinted brown. The more you put on it the more of an antique look you get.
220 is all that is really needed to sand down but 320 is OK. 320 will make it a bit smoother (not that after 3-4 coats of poly you will see much difference)