The fuel set up you currently have is prolly the best approach!
All you need is a suitable low pressure bypass reg up near the carb, the efi pump will like working with the lower pressure, it will pump more, work less, run quieter and last longer.
EFI pumps do NOT like or tolerate a dead head reg, it needs to be a bypass reg., typically they are a roller cell design or perhaps a gerotor and are a positive displacement pump, and seldom have any internal bypass system.
Go put a Holley Red or Blue on if you like noise and want to be broken down here and there and buying the occasional replacement pump...
As mentioned above, it could be wired such that the pump isn't powered at certain times, but why does it matter if there is no pressure while cranking, its prolly a good idea, a Holley carb will run for some time on what is just in the bowl, so will be plenty there once the pump is back in action when the key is in the run position. Another plus will be less load on the battery while cranking the engine.
If the fuel pumps that are there are neat and quality it would be a huge waste to throw them away just because there is a minor issue or someone doesn't understand the install properly.
LOTS of big HP cars (both efi and carbed) run EFI pumps, lift pumps and swirl pots, bypass fuel systems, its an ideal configuration.
Another benefit of having a bypass system with the reg at the carb/front is that as the car accelerates hard there are G's created that load the pump more, the fuel in the line may generate another psi or two that the fuel system has to account for, with a reg at the back this cant happen, but a bypass system, using a pump capable of more pressure than is needed, the bypass reg will account for the additional pressure to counteract the acceleration G's, so your gauge will show a constant pressure even under start line G's.
Just my two cents.
If you can't help yourself and pull the efi pumps out, at the very least use the Carter pumps mentioned above, at least then it'll be quiet and reliable.