I going to agree with Philbey here and suggest some sort of ignition cut instead of a fuel cut, for several reasons:
1, It won't be instantanious as philbey mentioned. You're going to need to drian the float bowl before anything happens. Ignition cut will be instantanious.
2, For aguments sake lets say your flat to the boards around a corner so oil pressure drops a bit and triggers the fuel cut. Lets also forget about the float bowl for a second.... what effectively happen to your motor..... its leant out substantially.... at the same time its being starved of oil as well! Again, cutting the ignition won't have the same detramental effect on the motor.
3, As you've already worked out youself you're going to have a chain reaction of failure while trying to start the car and would need a bypass of the fuel cut to get it started, mind you this would be the same case if you did go for an ignition cut. Maybe an idea for the compulsary for cut you need would be to see if you can get some sort of trigger off the alternator so the fuel pump does switch on until it see 13+V!? That way when you try and start it the alternator will make some charge, switch on the fuel pump and away you.... in theory.
At the end of the day this whole thing is just a band aid solution for the real problem..... the lack of baffeling and/or capacity in your sump.