My home cinema project is moving (slowly) forwards. Which was good as full HD projectors get cheaper all the time

But now I should start to choose one and have lots of unanswered questions.
The room is a cellar room with a 280cm high ceiling, length 680cm, width 500cm. As the room will also be used as a games(table tennis/darts) TV/party room for our teenage kids, my wife does not want it to have dark surfaces throughout. It has windows, but these can be totally blacked out as required. The screen wall will be black, the left wall red and the right wall, ceiling and rear wall white. The floor is a light maple laminate.
I want a
screen of 300cm (118") width and the (full HD) projector should be mounted on the rear wall – which means it will have a projection
distance (lens-to-screen) of around 630cm.
Now, having looked at a few sites and projectors, I am a little concerned about this. Most of the full HD projectors in the "reasonably affordable" category do not seem to have the power to project a 300cm image from this distance – even if the room lighting is completely off...
To improve things, I could just about persuade SWMBO that above the screen the first metre or so of ceiling could be painted black – and I could fit a dark carpet/rug below the screen which could be rolled up when not in use.
So, with all lighting off and the room dark around the screen at least,
which projector could come into question – and
what gain factor should the screen have for this set up (I've looked at various sites and am still not sure)?
Are the reviewers being hyper critical when they say projector X can't produce an good image wider than 240cm?
Anyone out there using one at above the recommended maximum and still very pleased? I suppose this is my main question