Maybe I don't know the problem well enough, but the relatively simultaneous nature of domestication seems like less of a mystery to me. More recent domestications (eg. in the Americas) seem to indicate that a hunter-gatherer population needs to be getting comfortable with a particular bioregion for at least a thousand years or so before an accumulation of of local knowledge can lead to the development of decent local cultivars. If this is a general and defensible rule, then I think our climate history can provide the rest of the evidence.
The ice age wasn't just cold, it was also chaotic, with temperatures pinging all over the place from year to year:
https://www.nature.com/scitable/knowledge/library/abrupt-cli...
In that context, any population would have had difficulty staying in one place for a thousand years -- I don't mean living a settled life, I just mean hanging out in generally the same bioregion. Bioregional adaptation would be detrimental in such an unstable environment: your tribe needs to stay mobile and highly adaptable, or it'll die. No chance to develop agriculture under those circumstances.
Eventually we enter a nice calm interglacial period, and settle down to do some fishing -- then spend the next thousand years being chased around by rapidly rising sea levels and mega-floods from bursting glacial dams.
Finally, about 11k-10k BPE, all that settles down -- although not without us acquiring some nice flood myths along the way -- and we have time settle down and start getting to know some bioregions on a long-term basis. A thousand years or so later, we've got agriculture popping up all over the place.
Seems like a reasonable story? Or am I missing something?