, you threw out such a hodge-podge of different projector models at different price ranges and with different throw ranges that it may have kept some from even responding and trying to deal with it. Obviously a case could be made both in favor and against every single model you listed based on price, performance, features and user preferences.
It would really help if you could narrow things down a little. For example, the 4k models you mention aren't true, 100% 4k but only have partial 4k capabilities. True 4k is still way out of your price range. That's why some are settling for good 1080p models and waiting for 4k prices to come down. Do you really want to exceed your preferred budget to get a model that's not 100% true 4k?
Then there's throw range. The Optoma GT1080 and GT1080Darbee are short throw models without a zoom lens. They must be a specific distance from the screen to throw a specific size image. For example, you mention a screen size of from 110"-130". Those two Optoma models can only throw a 110" image from a distance of exactly 3' 11" as measured from the front of the lens to the screen. If the projector is 3' 10" from the screen the image will be a little smaller than a 110" screen and if 4' from the screen the image will be a little bigger than a 110" screen. For a 130" image it would need to be exactly 4' 8" from the screen.
On the other hand the BenQ HT2050 can only throw a 110" image from a range of 9' 2" to 12' lens to screen depending on the amount of zoom used, and for a 130" image the range is 10' 11" to 14' 2". The other projector models you mention all have different throw ranges. So if you have a specific projector mounting location and screen size in mind not all of the projector models you mention are going to be able to do that.
You also have a mix of LCD and DLP models. They're different technologies with different strengths and weaknesses and some people argue over which is "best" like owners of Ford and Chevy pickup trucks.
So your original post is like opening a Pandora's box of conflicting options. For starters you would benefit greatly by doing a little research like reading basic primers on front projection comparing such basics as 3LCD and DLP and short throw vs. long throw as well as professional reviews of the models you might have interest in. Once you narrow your selection down a little it will be much easier for other forum members to make recommendations to you.
EDIT: I see that like magic you narrowed things down just as I was in process of writing the above.