Sub advice needed

If you go with four subs, they don't have to all be the same size or even brand.  I have two SVS SB13 Ultra subs and two Rythmik F25 subs in my 4 sub setup for my 2 channel system.  Completely overkill, but they are also used in my home theater system.

To the OP, you could get four Rythmik F12-300 subs within your price range.  It looks like you're using the Brooklyn as a pre-amp?  It appears to have two sets of outputs and your amp has only RCA inputs, so I'm assuming the amp is connected to the Brooklyn using the RCA outs.  You would need to get a couple of XLR Y splitters and then XLR to mini-XLR to connect the subs to your Brooklyn using the XLR outs on the Brooklyn.

You don't need a remote control for the sub's volume.  If your sub(s) is set up right, the bass will be there when it's in the music and it won't be when it's not.  You want to have the subwoofer set up to blend in the bass, not overpower the rest of the frequency range.  Once you have that, leave it alone.

big_greg, can the Ultra be used as a master controller to output its DSP processed and preset signals to slave non DSP subs?

Maybe?  It has XLR and RCA outputs.  I've never considered doing that.  The manuals should be available on SVS's website.

Are you able to simultaneously connect your two channel and your HT to the Ultra with the caveat of using the two channel or the HT one at a time?

I haven't done that, I'm using outputs on my two channel pre-amp to send signals to the subs when the HTBP is engaged on my two channel pre-amp.  Doing it that way I lose bass management from my home theater processor.  I'll have to give that a try, that would be a better solution than what I'm currently doing.