Fuel delivery issues

I'm probably going to replace the check valve on the brake booster
If you are refering to the valve that goes between the vacuum hose and the booster that would not produce the pedal to the floor that you experianced. The external valve only keeps vacuum in the canister. There is some valving inside the booster that must be malfunctioning.

For the moment you could cap off the vacuum to the booster and as long as you brakes work propperly you could temporarilly drive it that way.
. I'm starting to lean toward those additional 4 vent hoses being capped somewhere else in the system, so capping them off would be a priority
As long as you have a vented gas cap, capping them should not be an issue, as well as leaving them un capped for the moment( other than insects and dirt and moisture and fuel vapors)
If you think you are pulling a vacuum in the tank leave the gas cap off while testing