I had the same problem with fuel starvation on my FI BMW , and burnt out two fuel pumps as a result. The Fi pumps are great at pushing fuel but terrible at sucking fuel so any fuel surge leads to drop in fuel pressure at the injection rail.
To solve the problem I put the swirl pot and integral pump out of the fuel tank of the donor car into the fuel tank in the Cobra, carefully positioned the return feed so that it fed retuned fuel into said swirl pot and the result has been a complete cure of the problem.
Now I can run the tank almost dry and theres still not a trace of hesitation or power loss. Try to emulate the donor cars fuel system as closely as possible and you shouldn't have a problem.
Cheers,
Tony
