Thanks to both of you for the answers.
I did exactly that, but I didn't get much additional info, especially with "isodynamic". "Orthodynamic" basically points towards headphone boards and especially head-fi, while "planar magnetic" points towards speakers boards. I guess I'll have to go through the patent applications, and see if I can get anything from there.
Thanks for pointing that out, that's an interesting point from Yamaha. I don't know if that can be applied to other constructions (Audeze/HifiMan). The driver construction is different, isn't it ?
So far I have been able to find the following information :
1. Orthodynamic drivers are purely resistive loads, given their operation mode, different from dynamic drivers. As a consequence, they are not affected by the damping factor per se, as their impedance curve is virtually flat.
2. Given their construction (at least in the case of Audeze and HifiMan), and the lack of resistive load, it is necessary to keep a high damping factor. In other words, it is necessary to keep the drivers under control. This last point is interesting, but unfortunately I have nothing to substantiate it further, besides the fact that it's coming from K. Gilmore, on a different board.
3. Thread about Magnepans on speaker boards also point to the necessity of damping factor, to avoid driver "flapping".
So far, it seems like electrical damping is necessary to prevent the driver from getting out of control. From the Yamaha HP-1 brochure, we can see that an impedance of up to 300 Ohms is still ok, at least with that construction. Given that the impedance of the Yamaha is 150 Ohms, I suppose we could take a damping factor of 0.5 as the minimum acceptable. That is pretty low and a far cry from the 1/8 rule of thumb (I've also seen 1/20 recommanded).