I've never played with braille cards, so maybe I'm wrong here, but how can sighted people read what cards people have? Surely the braille is on the front of the cards, the bit that's face down? You could only read the braille with your eyes if you could read the print on the face of the card.

Anyway, there's an easy technological solution. A small device that is a computer with a hand-held scanner and OCR (Optical Character Recognition) software, and is effectively an electronic braille reader that's the size of a PDA:

They also have a reader to 'scan' their cards, and the dealer has one to scan the board cards. This wirelessly transmits to the reader so the player can 'read' the board whenever they want. It's not going to hold the play up by more than a few seconds. It doesn't even need to be a braille device, they could just wear an earphone and it could convert the braille/text to voice automatically. The scanners are very good these days, and are suitable for reading newspapers - so they would very easily deal with a pack of cards that have large characters on them in a standard format.
Very simple, very easy to move from one table to the next.
The most difficult element is the betting and counting of chips. But again, I'm sure there's an easy solution for that too.
Where there's a will there's a way - obviously the will isn't there.