The design of the mechanical pump should let you push right through it with a electric pump. It primes the system just fine doesn't it. When you say the eclectric will pressure up and run for a while, this is a sign of some other problem. If it was just the engine pump bad, the electric should get you around all day, that flat head won't use to much fuel or need much pressure.

Look for crap in the tank or filter. Don't try to suck through a filter, always push through, which means, don't install one at the tank!

Just more to think about, Joe.