I'm not following exactly what you're saying about the check valve, a picture might be better. You just need to replicate the feed it had on the bike.

Having a guess here, is the feed to the carbs a dead end from the pressure reg? If it's flooding after shut down either the pressure is climbing when the flow stops or the needle valves are not sealing properly when the floats are up. Stick a pressure gauge in the fuel line to the carb and watch what happens when you shut it off (low pressure range). You'll soon see if it goes up, holds steady, or gradually drops off. If it's a dead end line it should hold some pressure after shut down. What ever that pressure is is what the needle and seat can hold. If it goes up briefly then your pressure reg's the problem.

Also, 1psi is almost 1 meter of head (like having the tank 1 meter above the carbs) you can probably drop it some more. The formula is P = row*g*h or roughly P = 7*h kPa with h in meters for petrol 1psi=6.89kPa.

Have a cuppa and mull it over, you'll figure it out.

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I don't know if this helps but I think bike carbs are usually gravity fed (a handful of kPa, say less than 20kPa depending on how many Gs you can pull on a bike) so using a return line like that might help by keeping the fuel pressure minimal at the carbs. Certainly there'd only be a few kPa's at idle.

If you want a return line you'd probably want it to loop back after the carbs. Don't worry about check valves, the only place you might put one is in the carb feed to stop fuel draining back to the tank.

Ok found my datsun has the option of return line in efi and twin carb models.
Ive got another line for a return now.

anges old rotor ute and some carby rx7 have return lines from carb setups.

I also found in the spares from previous owner I have a return metal fuel pump to carb line. Like du fuel rail. Wont work with bike carbs as line now runs against fire wall not front of car like stock.

so reading up about bypass setups, using a t peice fuel will run to carbs and return line constantly its adviseable to put a one way check valve so fuel doesnt flow back into carbs.

the carbs draw what fuel they need.

does this sound like a viable option. Seems popular In jap cars to stop vapor lock?