Certainly Exped flat valves won't work.
Further consideration leads to the possibility of making an adapter by bodging a bit of tube into the valve closure lid from a dead Exped mat or pillow.
I have, somewhere, a 12V airbed inflator, that cost me a few quid from Wilkos (and, it turned out, could be persuaded to run from barakta's trike battery). This was useful when a cheap voluminous airbed was barakta's preferred camping mat. One camping weekend - Long Itch I think it was - it occurred to me that I might be able to use it to inflate my downmat. I experimented with wrapping a spare inner tube around its outlet valve in order to match the diameter of the exped flat valve, and simply holding it in place. The arrangement was fairly leaky, but the airflow was such that this didn't really matter, and holding something awkward in position for a while is substantially less effort than pumping up a downmat in the traditional manner.
Clarion spotted what I was doing, and offered a Snozzle valve adaptor, which gave a similarly functional but less fiddly to hold in place fit. I invested in one and used it to good effect until we bought barakta an Exped Airmat, which came with its own Snozzle.