In VLC, you can crop the 16:9 video into a 2.35:1 ratio, thereby removing the black bars.
That would still project letterboxed through a 4:3 or 16:9 LCD/DLP, and Bobajett is looking for a fully anamorphic source.
I guess the ideal here (while staying within the bounds of HD) is a 4:3 projector displaying 1440x1080, fitted with an anamorphic lens - this would sort-of approximate the behaviour of a film projector. Then it would be a case of recreating scope anamorphosis in the video source: crop off the black bars, and resize to 1440x1080 with a 2:1 pixel aspect ratio.
Since you’re more likely to be using a 16:9 projector, the maths are a little different - your projector (and therefore source) will be at 1920x1080, so the PAR for anamorphic scope would be more like 1.5:1. Which of course means that the anamorphic lens needs to be that ratio too, but it seems there’s already a market for this:
http://www.panamorph.com/home-theater-projector-lens/
Indeed, it’s supposedly possible to make your own:
http://www.zuggsoft.com/theater/prism.htm
Disclaimer: I’m definitely not an expert on this - I put up with letterboxed projections myself - but hopefully that’s a little closer to answering the question.