I think I need to go to Carter BBD Skool !
Just went thru similar with the BBD in my 1965 273. I knew it was running lean because it wanted to stall coming off idle. It idled OK cold with the choke closed and liked me closing the choke more as it warmed up. I couldn't test once warm since it wouldn't even idle long enough. I had to keep tapping the throttle to shoot accel pump gas to keep it idling and if I did that and held the throttle down a bit it would die after using up the accel shot. Going out on the idle screws didn't help much. I figured it must be a vacuum leak and suspected my current kludge of using the BBD on a 4 BBL intake w/ adapters, but flowing propane around there didn't help. After checking the booster hose, I thought to check the big PCV hose and found the purty aftermarket cap at the PCV valve off since its rubber gasket had fallen apart, which gave a massive vacuum leak (open hose). Amazing it even ran. Ran great after fixing that. It ran bad last time, but good enough to relocate the car in the driveways, so probably the gasket was partly cracked then. Problem was also confused because I found the brakes were locking up, due to having misadjusted the tip on the booster rod (piston didn't fully retract to open the fill port in the bore). Made same mistake on our 1996 Plymouth, but now have a booster measuring tool.