How should I wire a Trane air handler & heat strips?
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.