My understanding is that you can usually flash the BIOS from the BMC even if the BIOS is fucked, though it's a paid feature upgrade (though I think someone might have cracked the algorithm on older boards).

At least, it has been the case on several boards of mine, including an X10SDV which bricked itself, as far as I can tell, just from bad luck somehow.

I tried the BMC route, it didn't help.

As far as I can tell, the jumper dance was to enable the main BIOS to use the Management Engine controller to perform some other part of the flash, which would ordinarily be locked out with the jumpers in their normal position. But now that it's tried and failed, it won't try again, maybe?