Ive used both Michelin XS and Bridgestone Jamal (VSJ) on my Defender 110 and found both to be excellent. Their performance is biased towards soft sand (dune country) - thats when you get the best from them.
Equally Ive used agressive Michelin XCL and XZL in deserts, these are mud patterns and dig in, not good for soft sand (but not as bad as youd think either), but (esp the XZL) indestructible in rocky areas where XSs or Jamals would get sidewalls chopped up with rocks.
I have a set of Goodrich ATs that I am itching to try out, I think they will be a great compromise.
On non-LR vehicles (Toyota and Jeep) Ive used Dunlop Grandtreks (weak sidewalls) and Pirelli Scorpion ATs (not brilliant tread pattern).
All in all for deserts Mich XSs are a very good bet (they have the edge on Jamals, slightly), though watch sidewalls on rocky areas.
7.50x16 will suit the Rangey well, and *fit tubes*
'91 LR 110 Def/Disco hybrid "Elsa"
Bring me the horizon....