The speedometer gear is one of your problems. The vehicle speed sensor is driven by the speedometer gear, and if it isn't sending a digital signal to the EEC, then the EEC is always assuming that you're not even moving. I'm sure the EEC is really trying hard to keep the A/F in range, especially when you have a normal engine load, yet it is seeing no change from the VSS.
Get that fixed first.
As far as the idle bouncing, a vacuum leak will absolutely cause such symtoms, and
especially on your speed-density computer system!!! The computer relies on the MAP signal to determine load on the engine. Any leaks will throw this off, and almost without fail into the rich territory. If nothing else, you need to at least PLUG those melted hard vacuum lines, and ensure that there are no other leaks anywhere else. Good luck.