Hi Ven, I would use Polyacetal sheet available in both black and white. This can be bought on eBay in 8mm thickness and various sizes under " ACETAL SHEET ". it can be machined eg. turned, milled, drilled and and tapped. It does not adhere very well in my experience, but the letters could be as you suggested tapped and held from the back using screws. I would not advise raising the letters for cleaning, where I live it would quickly provide a home for spiders.
Good luck
Cheers David