I'm wondering if you have considered something like Classflow Connect which mirrors the primary class display?
click here the school budget can cope with this is another matter!
I too had a difficult classroom. In the end I had to re-orientate my room so that my projector displayed in the centre of one of the two long walls. It worked quite well and I didn't have the problem of having half of the class with their backs towards me whilst they were watching a presentation.