@OyyoDams Wow, I think that you nailed it !
I finally managed to get the SFC30 working after a firmware upgrade (my version was 2.67, since your URL stops at 2.62 I looked around - and found version 3.0 here: http://download.8bitdo.com/Firmware/GamePad/)
Everything worked like a charm: I could start the pad with Start (only), pair it, configure it and use it in a game.
I'm now doing the same with the SNES30, a priori I can use the same firmware. There is no reason this should fail.
So THANKS A LOT to both of you, @Substring and @OyyoDams for having taken the time to help me. I hope this post will help other users as well.
Keep up the excellent work !