Issues with a rebuilt 360

that's not how vacuum secondaries work, they work based on vacuum at wot. your brakes work on idle vacuum which as you say drops off with a 'bigger' cam.
neil.
Lets clarify this.
Vacuum secondaries get their vacuum signal from velocity of the air flow. On some carbs this is amplified slightly by a tube with a angled tip in the primary side.
There is a connecting passage into the secondary side. At first this bleeds off the effect on the vacuum diagphram, but once the air is flowing in the secondariy side, it increases the pressure drop.

Much more detail here. Read all the pages. Lots of info in there.
Vacuum Secondary Diaphragm Signal Tube