The main problem with projecting 16:9 content on a 1:1 screen is that while you will have black screen borders on the left and right, the top and bottom will have vacant white screen that will show up as light grey when a 16:9 image is projected. While this is not ideal for watching movies in a home theater, it's not as critical in a conference room, which I assume will be primarily used for presentations.
Will all content you will be projecting be in 16:9 format? If so there's a positive for a projector that lacks vertical lens shift as you will not be trying to precisely square up a 16:9 image in a 16:9 viewing area. That means projector mounting height is not as critical since you will have 6.5' of vertical image space and your 3' 8" image can fall anywhere within that 6.5' vertical window. In that case you could simply lower the screen to the point that the bottom of the image lines up with the black border on the bottom of the screen so that you would only have white space at the top of the screen.
You didn't mention how bright a projector you need. At their brightest settings the BenQ models will work pretty well in a reasonable amount of ambient light. However, if the conference room is brightly lit during presentations you might need a brighter business projector. That would require additional research as bright, short throw business projectors with 1080p definition might be hard to find.
By the way, for conference room use it would be an advantage to go with BenQ's newer HT2150ST over the older HT1085ST as the newer model has a revised case to reduce fan noise and light leakage that would make it less distracting during presentations.