Well...you're going to have a little bit of a problem towards the end with induction but I kind of like it.  May have potential.

I have made a drawing here, and not tried this out before. Is this worth trying?
The iron is present to hopefully get the magnets in constant magnetic imbalance - which hopefully make the wheels spinning in the opposite directions to each other.
Please see the picture for details - and for those who can, imagine how it will work:

i just don't know

Do you believe the induction problem could be reduced by using a non conductive material instead of iron?
Like iron powder, ferrite material or similar non conductive materials?

I have previously discovered that when letting a neo magnet glide down a massive aluminum plate, it glides very slow due to counter induction in the aluminum - that is holding the magnet back. The same resistance will probably give some problems in such rotating device (?)

Hi,

Yes, I think you see this eddy current problem correctly. But it can be minimized by using either ferrite (but it is difficult to make the needed shape, maybe you can build gradual steps from ferrite blocks) or laminations like mains transformer cores.
BUT eddy current is a 'small' problem with respect to another one what  acp hinted as cogging.
Indeed there is the sticky spot where the two almost facing repel magnets are about to leave the shield. Much much experiment is needed to figure out the best compromise as to shield material thickness in that critical area, distances involved and all this is matched together to get the smallest cogging  (=sticky point=counterforce) possible.
And the biggest question is: when you achieved this best situation by hard experimentation then the system has got enough inherent  kinetic energy collected from the attractions to defeat that counterforce???

It would be easier first to tinker with one rotary disk with the magnets on it and sense the counterforce by holding one repel magnet in one hand and holding / changing different iron pieces (thinner and thicker ones) in your other hand, not to bother with eddy currents first.
Several variants of your setup already appeared either in this Forum or in some older patents too. Even a small electromagnet was used just at the sticky point to defeat the counterforce, switched in only at the right moment, once in every 360 degree rotation periode. Unfortunately, I have not seen any report what was the mechanical output power of such motor with respect to the electromagnet input power?  Surely it does seem promising: you consume input power during a few percent of the full rotation time and attraction forces of the magnets work during the rest of the rotation periode.
OR is it decisive?

Regards
Gyula