Won’t start

Mattax said
No need to look further. Unless I've misunderstood, its siphoned though the boosters or leaked down after this

So the needle valve wasn't shutting the fuel off even when overflowing.

That would also goes along with the fact it was almost starting when the throttle was held open.

Those instruction have confused everyone forever.
Here's the deal. The spring adjuster should be just touching the pump lever at slow idle.
Then, when at wide open throttle the lever should have enough play in it when pushed further that a .015" feeler gage can be slipped in. The purpose is to be confident its not bottoming out the pump diaphram under normal operation. Even if it is bottoming out, the spring has, or should have, some give in it; so its not the end of the world.

So I found the reference number on the air horn its R6910. It’s not on the reference sheet you posted or the one I have. I googled it and according to Holley that number belongs to 4165 800cfm carb. And the other number on the choke housing though suggest it’s a 4160. Could this used carb be a mixed match parts carb and that’s why I’m having issues getting fuel out the front booster? I’ve attached some pics for reference.