Hi Cosmicma,
Thank you very much for you answer. Obviously, it's not a very satisfying one. I guess the good news is that I'm not doing anything wrong, per say. The bad news in your answer is that it's VERY dissatisfying that I've bought a studio system that, after all the rave reviews in its class, doesn't seem to be up to the job.
Anyway, it clears things up bit, and I guess I can work with 1/125th, but it's not optimal when working with babies/kids, as they move around so much. It won't be a problem for the adults, though.
I'll try Canon and Elinchrom support, to see if they can help me with a better solution.
Thanks again.
Cheers...