In your situation I’d consider this Anthem AVM50 prepro. It’s got a decent preamp section, but maybe even more important given your limited speaker placement options and sub you might find Anthem’s room correction and sub integration capabilities to be very advantageous -- perhaps even more so than going for a more pure 2-channel pre. Best of luck.
https://www.ebay.com/itm/192921906325?ul_ref=http%253A%252F%252Frover.ebay.com%252Frover%252F1%252F7...
If you’d like to try tubes you could do far worse than this Backert Rhumba for a little over your price target...
http://www.echohifi.com/details/13757/Backert-Labs_Rhumba-1.1
or this Sachs SP14...
http://www.dsachsconsulting.com/custom%20line%20stage.html
https://www.ebay.com/itm/192921906325?ul_ref=http%253A%252F%252Frover.ebay.com%252Frover%252F1%252F7...
If you’d like to try tubes you could do far worse than this Backert Rhumba for a little over your price target...
http://www.echohifi.com/details/13757/Backert-Labs_Rhumba-1.1
or this Sachs SP14...
http://www.dsachsconsulting.com/custom%20line%20stage.html