I haven't done the deserts on my Tenere, but I have a couple of ideas that might work for you because I have done the Great Victoria on an early TE610E, and the Simpson on a WR426. Plus I do a lot of sand riding at work.
First, I'd make sure your suspension is as good as you can make it. Riding sand on a soggy bike is very hard work.
Second, if you can find one, I'd fit a 3.25/3.50x21 Cheng Shin. Not great on the road, but really good for reducing pinch flats and rim damage, not to mention widening the front tyre's footprint. If you can't get one, fit the widest and highest 21" tyre you can find. Also, I suggest fitting security bolts so you can run lower pressures. You'll be surprised how much tyres can slip on the rim, even in sand.
Hope this helps. Fwiw, I think a Tenere would do the job fine, but you need to be a confident sand rider or I would think twice before doing it. It can be hard work. If your speed falls off too much, you might too! Don't ask how I know this. My secret is safe with me!!