So... Long night, nothing to do, decided to install an evaluation of Win 8.1 + updates to see what MS was up to.
This problem is reported to MS IE team shortly after the release of patch kb2976627
One month past and another round of patches but unfortunately this problem hasn't be solved. :cry:
Anyway, here we are... I'm with the '627 update (the one you mentioned), the rest is pure unmodified stock English Windows 8.1, and it's working just fine.
I'm currently installing all other updates (excluding the other ones for IE11 which I'll do much later), so if I can then reproduce, it means it's not due to '627, but to some other Windows update.