
Valerion
VisionMaster Pro 2
Great picture/gaming, but RBE and no lens shift are dealbreakers.

Running these analyses costs money. Buy through my links to help keep lights on! I may get a small commission.
You are losing a fair bit of quality by simply projecting on a wall unless you put in a lot of time and effort making it into a good screen. Keep that in mind. I think you've done good homework on things already. These models aren't miles apart from one another. The Valerion is probably the way I would go if it fit my space and was within my budget. That or the XGimi Horizon 20. In recent testing, the Horizon 20 Max was praised for image quality, but was considered too expensive for what you get. I tend to agree. At $3,000, I'm looking at the XGimi Titan Max, currently on Kickstarter. But, if I'm buying in that lineup, the standard XGimi Horizon is a incredible value and is plenty bright enough for a 120" diagonal or so, if it fits your room, I'd look hard at it. Not sure what about the BenQ really sets it apart from the competition. It's a good model, and the short throw lens is nice. BenQ has been playing a bit of catch up with XGimi and Valerion in recent years. But, they have been doing it for a long time and they aren't doing stupid things. Models like their X500i are very solid home theater models and the LED light engine eliminates laser speckle. But, it's not bright enough and would leave you asking for more I expect.
I just upgraded from 1080p Epson 2150 to the horizon 20 base model. I have a dark basement so didn't need the extra lumens. I love it so far, super bright and crisp
I’ve got 110” screen with a projector that’s only 1800 lumens and it’s too bright sometimes lol. I think you’d be okay. You can always send it back if you don’t like it. I did that with the original horizon before i got this one. Perfectly good projector, just poor black levels for me
Good news, your expectations are super reasonable. Do you want one with a built-in OS like Android or are you happy just throwing a Fire Stick or equivalent in for streaming movies? XGIMI has refurbished models on their website around your price point that'll likely exceed what you're looking for, and you can very likely find a used BenQ or an older-model Valerion around there too.
You should be able to get the XGIMI Horizon refurb on their website around that. It's what I'd be using if I hadn't gotten a great deal on my TK710 this summer (Amazon Prime deals can be a heck of a thing if you get lucky)
There are still good deals on some of the Xgimi models for black Friday. Some of the slightly older models in the Horizon line are 700-800 and offer good features and quality. They run Android TV but don't have Netflix for some certification reason (can always add a stick).
We currently have this one https://www.bol.com/be/nl/p/xgimi-horizon-smart-projector-beamer-harman-kardon-2-x-8w-luidsprekers-chromecast-1500-iso-lumen-dolby-audio-bluetooth-dts-h/9300000044603293/?Referrer=ADVNLGOO002013-S--9300000044603293-PMAX-C-22290424073&gad_source=1&gad_campaignid=22294182655&gbraid=0AAAAAD5OnmPlILNzP11NiqlX2MtiWrlqW&gclid=Cj0KCQiAi9rJBhCYARIsALyPDts1akWALTyWymsIadPHF43_jL_Kkimu6EWjVmg1IzPJ8DNfdxi53CIaAuGMEALw_wcB But we have also had the Halo+ (is think) before that. We are verry happy, this thing runs Every day for hours on end (im partial insomniac, so spend most time watching shows and movies on Plex). This thing is great

Valerion
VisionMaster Pro 2
Great picture/gaming, but RBE and no lens shift are dealbreakers.

Epson
Home Cinema 5050UB (V11H930020)
Great value with huge lens shift, but outdated lamp tech and poor HDR.
Epson
Pro Cinema LS12000 4K PRO-UHD Laser Projector
Superb 4K/120Hz gaming and no RBE, but requires calibration.

BenQ
W1070
Budget king, durable with good image, but RBE can be distracting.

BenQ
HT2060
Excellent 1080p contrast and quiet gaming, but low brightness for big screens.

Ranked #1
Valerion - VisionMaster Pro 2

Ranked #1
Epson - Home Cinema 5050UB (V11H930020)

Ranked #1
Hisense - Laser TV PX3-PRO

Ranked #1
Anker - NEBULA X1 4K Triple Laser Projector (D2351)

Ranked #1
BenQ - GV50 Portable Projector

Ranked #1
Anker - Mars 3 Air