Using the tag "reverse" at Myfonts https://www.myfonts.com/search/tag%3Areverse/fonts/ produces a fair number of fonts that you might wish to test on screen.
Don

Verdana and Georgia are designed for screen use and have lower cases -- unlike most of the fonts in the reverse tag list above. I don't know if a reverse/negative version is available. The Bodoni on the list has a lower case, but it is very high contrast and might be difficult to read.
Don

You may want to have a look here: http://clearviewhwy.com/

The stroke width will appear differently for positive and negative contrast, but that doesn’t mean that you would choose a specific design for a certain type of contrast.

And regarding the design: It would heavily depend on the perceived font size and the resolution of the projector. If the perceived font size and the resolution of the monitor are large enough, you might be able to go with almost any kind of type design. But if the font size gets too small, you need to get low contrast (regarding stroke width changes, x-height, counters, serifs …). If the resolution gets too small, you would need to consider screen-specific effects, which fonts like the already mentioned Georgia and Verdana master quite well. The operating system or app and their render engine also heavily effect the outcome when very few pixels are used for each character.

FF Transit was designed with this aspect in consideration, eg adaptation of glyphs to compensate for glare and such. It is a quite modern typeface and may not suit your taste (I like it, though).