360 driveability problem

Sounds like you have messed around with the timing quite a bit, to include the timing chain and gears and distributor, you say no notable changes, in my opinion, time to move on.
You mentioned very poor idle quality, engine shaking, etc. Did you try to "smother" the carb like I suggested, there are a million places to develop vacuum leaks, you need to rule this out, my method is quick and simple and if nothing else, will eliminate vacuum issues from the list of things to try. If and when this fails, there is always the next step...... Don't give up though, as frustrating as it may seem, you will find it, and when you do, you'll probably kick yourself. As far as fatherhood, I have 5 kids, know what you're talkin' about!!!