If I make them invisible, what unit should detect them?
Thopters should detect invisible units.
In desert they can ambush incoming transports, and are less vulnerable to being picked off by thopters.
Instead of the heavy tank, give them an anti-tank infantry unit in the same tech slot; this is what I meant by "replacing some of the mechanized units with UUs".
Not just something with the same stats and a different art; as you say, that wouldn't make them play differently.
It plays different because:
a) they won't have the mobile armor units. They will have very poor mobility on land.
b) They won't have the really high strength of the highest power tank unit, though that is very late game indeed. They'll should have a unit that can defend against it (some kind of anti-tank trooper) but not one with the same offensive power.
c) They won't have aircraft, and the ability to soften units up with those, and their general utility.
d) They won't have decent siege units, but lots of their good infantry ignores city walls.
However, they will have larger cities (water bonus from buildings), and better infantry, and a much greater ability to act as raiders. Pillage enemy stuff, then retreat into the desert, where the enemy can't follow (or where you at least have an advantage).
They shouldn't be able to match in sheer on-land brute force strength, thats the point.
You could add a base 10% combat strength onto the Fremen promotion too to signify their general superior training.