While I am all for ditching the Zeniths, if the Webers aren't in the budget right now, there is no reason why it shouldn't be possible to get the Zeniths to function properly for now. It sounds like your experimentation has paid off with substantial improvement in how the car runs. Keep experimenting with small changes in the timing and carb settings.
Something that occurred to me was that if the engine idles smoothly, it's unlikely that you have a burned valve. A burned valve would manifest itself as a regular (not erratic) misfire at all engine speeds, accompanied by a "chuff, chuff, chuff" sound at the exhaust each time the affected cylinder misfired.
If the car runs normally until the gas pedal is about halfway down, then starts to act up, the secondary sides of the carbs could be lean, or not opening for some reason. Once the throttle is about halfway depressed, the vacuum-operated secondaries should start to open. If the engine acts up at all engine speeds above idle, this is probably not the problem. Keep working on it, and sooner or later you'll solve this riddle.