If you are still running the old version of the DME relay (944 part number) it should at least be put in the glove box with a note that it might not work 100%. The newer ones, 993 part number, have been reliable for me over 4 cars and 20 years but if I were in the market I'd probably get the solid state version now.
DME Relay Information and Testing
The Focus 9 Solid State relay seems pretty bulletproof but but keep a spare relay and/or a jumper wire on board. My choice would be without pump priming as a few cranks to build oil pressure when cold seems like a good idea.
Not sure if the DME relay is your problem but a problem like you have is a lot harder to track down if you have the old DME relay. You can try the jumper wire in the meantime to see if the problem goes away.
-Joel.