I don't think an avgas engine would even run, never mind start, on avtur or diesel.
BTW I don't believe any imminent demise of avgas. There are tens of thousands of avgas planes around the world. About 1/3 of avgas burnt is burnt in engines which cannot run 96UL or similar. Some very good replacement fuel will need to be worked out, and probably retrofit fadec / electronic ignition systems will come in too, for some engines.
You can probably run an avgas engine on a mixture with maybe (at a wild guess) 10% of avtur because the stuff is bound to be soluble in avgas...??