After I read through the whole thread I was amazed that no one said to look at the carb. Which is the problem; you and your friend figured that out with the one you borrowed.
It's not the cam, and its not timing; the idle circuit on your 1405 carb has a problem, either not enough fuel or too much fuel. When you adjust the idle screw all the way in you tip in the butterflies and start running (idling) on the part throttle circuit, which with enough throttle opening overcomes the idle circuit fuel (too much/too little) problem.
The good news is the 1405 is an easy rebuild, get the kit and a (big) can of gunk. Disassemble the carb, put only metal parts in the gunk and soak overnight (up to about 24 hours).
After soaking I like to spray out the carb and pieces with gumout carb cleaner. Then reassemble the carb using the gaskets and other items from the kit.
I do agree that you should get a timing light and verify your timing is set correctly. It's been a while, but I thought the 1405 carb had connections for both ported and unported vacuum. The vacuum advance should use the unported (manifold) vacuum.
If the vacuum advance is working properly, and the distributer is stock, don't worry about the advance curve springs, just set the static advance, and check the total advance. The curve setting is for high performance, but you wouldn't notice much difference on a daily driver.