About a 7.1 vs. a 7.2 receiver, it depends on the receiver. Most 7.2 receivers ( all the cheaper ones ) just have the signal Y'd on the inside of the receiver, which is the same thing as just buying an external Y adapter. Now a few of the better 7.2 receivers have Audyssey Mult EQ XT32 which EQ's/Calibrates the 2 subs individually, all other receivers just act as its one subwoofer. So unless you are going to spend big money on a 7.2 receiver it really doesn't matter which you get. But remember you should spend less on your receiver than on your sub(s) OR speakers. So many times ppl buy expensive receivers then buy cheap speakers and sub(s).
Next best thing to upgrade would be the sub. You have to decide what your goal is to know if you should buy a single better sub or buy a 2nd F12. 2 subs placed at very different locations in the room will help get even bass thru the whole room so everyone hears the same bass. 1 better sub might have more power and be able to dig much deeper than 2 - F12's. IMO if you want a single sub I would be looking in the $500 - $800 price range with subs like Rythmik LV12R, Outlaw Audio LFM-1 Plus or EX, Hsu VTF2 MK4 or VTF3 MK4, Power Sound Audio XV15, SVS PB12 NSD or PC12 NSD. If that is too much money then get a 2nd F12.
The other thing you could do is just do 7.1 from the start. Don't take the BS22's back, keep them for your rear surrounds and just add the FS52's for the front L&R.