National Electrical Code 2014

Chapter 3 Wiring Methods

Article 300 Wiring Methods and Materials

I. General

300.3 Conductors

(B) Conductors of the Same Circuit. All conductors of the same circuit and, where used, the grounded conductor and all equipment-grounding conductors and bonding conductors shall be contained within the same raceway, auxiliary gutter, cable tray, cablebus assembly, trench, cable, or cord, unless otherwise permitted in accordance with 300.3(B)(1) through (B)(4).

The hot and neutral wires should be in the same raceway to reduce Inductive Coupling. You'll see using the Right-hand rule, that the magnetic fields created by the hot and neutral wires tend to cancel each other out. Thereby reducing the affects of inductive coupling.

I = current flow direction. B = direction of the magnetic field.

The ground wire was required to run in the same raceway, to provide a safe path for electricity to travel in the event of a short. If one of the wires sheathing becomes damaged, it's likely the exposed wire would have come in contact with the ground. The same way an equipment ground provides protection at a consumer, running the ground in the same raceway provides similar protection the entire length of the circuit.

Unless I'm missing something in your explanation, using the 2/0 AL wire doesn't seem to be a problem, except that it's AL and the unit does not specify AL. What will probably be simpler than running all new wire is to just get AL-to-copper splice connectors.

And in response to:

if I run two separate circuits/lines, do I need to tie together to the (2) 240 volt 2-pole breakers

No, you don't. If the heater circuit trips, you'll just lose your heat. And if the air handler breaker trips, it will shut off the heater strips. So no problem there.

In response to your update:

If the breaker is visibly damaged, then replace the breaker. If you decide to keep the AL wire, then make sure the breaker is rated for AL. Again, replacing the breaker will be cheaper than running all new copper.

A partially melted lug is a bad sign. You need to get an evaluation from a professional.

Having two breakers is still not a problem. If breaker for the lone heater strip trips, you get reduced heating capacity. If the other breaker trips, the air handler will shut off the other heater strip automatically.