The biggest issue with what you're looking at is that these single chip DLP projectors have HORRENDOUS color accuracy at their full brightness and once calibrated are far less bright than what they advertise. More in the range of about 1/3 of their peak potential brightness. This is important to keep in mind if you are looking at DLP models vs. LCD models.

In fairness, you are looking at smaller models, and the reality is that when you get LCD projectors of actual 3,500+ lumens in brightness, the size goes up a fair bit. Same with DLP projectors which actually deliver on their claimed brightness specifications.

Larger projectors aren't necessarily noisier. The larger fans can spin slower, or at high brightness, they tend to emit a lower tone than smaller fans in smaller projectors which can have somewhat whiny fans.

That said, the Casio models aren't horrible. They just aren't built very well which is why they no longer make projectors...
https://www.casio-intl.com/asia/en/projector/

I would avoid them.

Frankly, some of the best deals can be found on eBay on used business class WUXGA projectors. Yes, they use lamps instead of being solid state (most of them) but you can pick up 5,000 lumen WUXGA projectors for under $500 that are in good working condition.

Going a bit higher in budget also nets you some very solid LCD projectors that I'd look at over the DLP models...
https://www.projectorcentral.com/projectors.cfm?g=2&br=3500&br=10000&ar=Wide+%2816%3A9-10%29<g=101&dt=1.0.0&p=500&p=1500&exp3=1&oop=3&sort=%24#list

This model specifically jumped out at me as it is really bright and hits all the marks pretty well. It's also 1920x1080 resolution, which is a nice bump up from the mostly 1280x800 models on the list.
https://www.projectorcentral.com/Epson-Pro_EX11000.htm

Be aware of your throw distance (lens to screen) and if you need a model with shorter throw or some other specific feature to hit your target screen size...
https://www.projectorcentral.com/Epson-Pro_EX11000-projection-calculator-pro.htm

If looking at used stuff, Panasonic has a fair number of models they have had on the market for a number of years now...
https://www.ebay.com/sch/i.html?_from=R40&_nkw=panasonic+laser+projector&_sacat=0&_sop=15

In my mind, I'd go used almost all the time in this type of situation. The resolution of 1920x1200 has been around for a good decade (or more) with projectors that are quite capable and look quite good. The ability to pick them up for not a serious amount of money is crazy.

You don't get the warranty of a brand new model, but you get them for half (or less) the price of something new.

Be aware, projectors bumped up against one another do struggle to match their color exactly. This is far more difficult to do than people believe. When displays are NOT side by side, you'd swear they all look the same, but when they are put side by side by side you easily see how completely different the exact same model of projector looks.