I wouldn't worry about the re-circ door. How often do you really use it? If it does break, you can just take it out through the blower motor hole.
I would go ahead and pony up for the heater core though. It will not be any more work.
That said, if you have maintained the cooling system with proper flushes and fluids, then with 165K kms, I would think it would be in OK shape if you want to leave it.
if you do not know the history of the cooling system, or you did not maintain it, go ahead and spend the extra and replace the core. If the system was maintained, leave the core alone.