IMO, if you can demo and see the RS46 it is in a completely different class than the others. You also have position requirements you are trying to reach for your screen size which may not be accommodated by the cheaper projectors, forcing you into a more expensive model.
The HT2050, by example, while an excellent entry level model, can only hit a 120" diagonal from 10' to 13'1" lens to screen, and it sounds like you want to be about 18' lens to screen (or so).
Be aware, that 18' lens to screen is outside the range of many entry level projectors.
Off the cuff, there are only 4 models which show up on the PC Database which can hit that size from that distance for under $1,000.
You just aren't going to do better than the RS46 for that type of money, the price is in line with the quality, and as long as it is working, it's a great choice IMO for a new model.
There is a lot of JVC talk in the over $3,000 forum which you should read through. It's not the best for gaming on, that's for sure. It handles 120" just fine, but it cries out for as dark of a space as you can possibly make the room. Walls, ceiling, and carpet as dark as possible with no lights on for best results.
I would probably move the mounting location up several feet.
You also may find your screen size 'small' for your viewing distance. Typically for 13'-14' eyes to screen a 130" to 150" screen would be common.