Help me spend $1500-$1800 on a new set up

I currently have a basement home theater which is 28x12, with battleship gray walls. I would like to upgrade the 2004 Mitsubishi HD RPTV which is 1080i through its DVI port, I run all my sources through my Yamaha receiver’s HDMI port (hdmi to dvi cable). I have looked at 3 different options and would like pros and cons of each if possible. The first option is a 73 or 82” Mitsubishi DLP, I know they are no longer made but several sellers still have them for between 1100 and 1800. The second option is a 70” Vizeo LED I have seen for 1700 (there may be other flat screens in that price range also). The third option is a projector and screen. I have looked at the Epson 8350 and the Mitsubishi HC4000, each PJ is around 1150 and the screen I looked at was 350 (110” rigid screen that I would mount to the wall). The PJ would be ceiling mounted about 13’ from the screen directly above a couch used for theater seating. My viewing habits are as follows: 40-45% cable viewing (Cablevision of New York @ 1080i), 40-45% video gaming (xbox 360, also HBOGO on xbox ), and the remainder blu-ray, hddvd, and dvd viewing. This system would be used an average of 4-5 hours a day (2-4 weekdays and 6-10 weekends). Any suggestions are greatly appreciated.