Rear projection takes away from image quality slightly. But, it doesn't impact image brightness really. You get some transmission loss as it passes through the material, but if you are able to isolate the rear projection area in 100% darkness from the area in front of the screen with ambient light, then you will maintain much higher contrast on the viewing side of the image which could be of great benefit.

If it is open behind the screen and ambient light gets in, then don't bother with rear projection would be my recommendation.

Likewise, grey screens don't do much to increase contrast, but they do a fair bit to lower overall brightness. It creates a better black floor, but you lose the white highlights a bit. I would not go this route. Instead, I would shoot for a projector capable of delivering more light output.

I have a problem with any place using a single chip DLP projector when they are presenting to such a large group of people. I would stick with 3-chip technologies. 3-DLP is what theaters use, 3-LCD is great for those more on a budget. LCoS is also great, but rarely as bright or within budget.

I would definitely put Epson on the list of potential products.

Consider a model like this:
https://www.audiogeneral.com/store/products/view/0600-6093-U

A factory refurbished model with a 3-year warranty and a laser light source and interchangeable lenses. You will be able to cut light output to your screen for watching films, while boosting light output WAY up to what you need for when the lights are on.

The 3-chip design will eliminate RBE issues and potential headaches for viewers and the laser light source will maintain brightness over time. Plus, Epson has a great service department just in case there ever is a time when it needs to go out for repair.

If this is 'above budget', then what are you doing?
Seriously, if this is for a film festival, then the device that plays the films back is by far the most important thing you can have here. Get a decent screen to last 10 or more years, and get a projector designed to light it up properly. It will make the crowd happier with their experience.

3-DLP is WELL outside of your budget. That's what commercial cinemas use.

I would use a 3-chip technology, and while 3-DLP is nice, it isn't affordable. 3-LCD, from Epson, NEC, Panasonic, Sony, and others is affordable and is very typical for many installations.

Also, be aware that boutique brands, like Barco or Christie, have some very nice projectors, but you often pay a fair bit more for the same quality that others produce for less money. You will pay a lot more for the repairs that go with some of those models.

I do recommend not only 3-chip technology, but the use of a laser light engine will reduce the total cost of ownership. Potentially significantly if you replace lamps regularly.

Otherwise, yes, a model you can dim and raise the light source for can help with different ambient lighting situations.