Definitely thumbs up on the Richman book. It's quite strange to the uninitiated - it contains virtually no material, but presents a set of exercises designed to develop certain skills in isolation. The claim is that these skills are the 'core' of what is required to be a good sight-reader. Once you can do them individually, the rest is just integration and practice.
If you can read music already, then don't be put off by the first few pages (they explain musical notation) - the meat of the material is towards the end. Unless you're a rehearsal-level reader, I imagine it would teach you something. If you're teaching students to sight-read, it almost certainly will provide food for thought.
You'll also need a copy of Bach's 371 Chorales (Riemenschneider ed) - must be on 2 staves.
My story for what it's worth: I'm already substantially post-g8 violin, so no problems with the notation. However, my "vertical" reading was appalling - ie exactly what's required for the piano. I find it best to work on Richman and sight read something every single day. Starting a year ago, I went through a hymn book, Clementi Sonatinas, a pop-song book, a book of anthems for choirs, Haydn's Creation. I'm about to print off the vocal score for the Marriage of Figaro and start on that. (Aside: thinking up ideas for enough material is part of the challenge. You simply have to find new notes to play every day, or it isn't sight-reading).
Don't get me wrong: my reading is still pretty awful. The orchestral reductions (eg Creation) sometimes lie very awkwardly under the fingers. The fast movements I'm often taking at 1/3 performance speed or lower. However, I get most of the notes, I don't collapse too often and I'm light years ahead of where I was 12 months ago.
Will I get to be decent at SR? - that is, one of these pianists able to sit down at a rehearsal and just let the notes flow out...I don't know. My experience is that it's going to take many, many years. Even if I never get there, I'll have seen a lot of notes along the way.