Hi Louis - good first post. The right questions and to the point.

If I were hitching back with a bike I would sooner try it from Dakhla because there will be more traffic, the request will be less unusual, there will be buses (and even planes) so it will be all round less expensive and less complicated.
Or try just inside the Moroccan border - plenty of stopped vehicles.
Also, I'm sure you know you don't need a truck; a bike can be chucked on the roof of any car, pickup etc. Even a tourist motorhomer might help.

I have never been to Zouerat but I am pretty sure the mine/s are not open to tourists (like they are in Western Australia, for example) unless you meet the right person. But I still think the towns could be an interesting 'wild west' outpost to visit, not just the mines.

You are right about the 'Eye of the Sahara' from ground level. We were there in the late 90s before that description had been invented and from the central point all you can see is low hills all around. Nothing special at all, plus I'm not sure you'll be able to cycle the sands to get there from Ouadane before running out of water. Even in November Mauritania can be hot.

Consider: Choum, cycle down to Atar, head on to Terjit.
Back to Atar then out to Chinguetti and, if you can handle the track, on to Ouadane.
Both are interesting old Saharan towns.
You could probably get a lift back to Atar on a carrot pickup, but expect to pay. Hitching with locals is not usually free in the Sahara.

Or, if you have an MTB try a loop: Atar, Terjit, junction off new Tidjika road for Mhaireth (piste, 15km from jct). Then if you feel confident, carry on out of the canyon and NNE to the Atar-Chinguetti track just above the Ebnou pass (about 40km) where the tarmac soon starts, and freewheel back down to Atar (25km). On the way you will pass stromatolite fossils by the road, the original life form that oxygenated Earth x billion years ago. (Unfortunately, that makes them sound more interesting than they look).

Will be a good mini adventure but just remember, what sounds easy and exciting at this stage has a habit of becoming much harder once you're actually out there, especially after 8 days of Atlantic headwinds.