OK my LX BB has just given up the ghost. So rather than just relpace the BB I've bought a new SLX to replace the OEM Deore crankset. However, the rings on my Deore still have a bit of life in them (and I'd really like to suck all the life out of them and replace the cassette, chain and rings in one go when the whole lot is worn) – can I swap the Deore rings to the SLX? Also are the M770XT rings compatable w/ SLX?

yes. (to both questions)