I'm guessing you mean the JDM dual-DIN kit that has a replacement HVAC panel (even if you've installed a new single-DIN head unit).
Do the digital temperature displays on the HVAC panel still let you dial in different numbers? In other words, does the HVAC panel visually still look like everything works? And does your car only run the A/C compressor at appropriate times (e.g., when you dial in a temperature lower than ambient, or when you use the front defroster)?
If that's the case, the problem may simply be a fault with the air mix doors and/or the servo motors behind the dash. Search for threads here from people who had that issue.
Also, the OEM HU/HVAC unit has diagnostic modes that you can use to test the car's HVAC system. See Subaru's service manual for details. I don't know if the JDM HVAC panel uses the same keypress sequence to access that mode (if so, it will be like what you do on the OEM HU in a 2008 Legacy or Outback).
ADDED: Also, you can't do either of the things you asked (swapping the driver and passenger controls, or ganging them onto one knob). The HVAC panel (or HVAC portion of the OEM HU) simply sends commands to a separate A/C control module behind the dash. See this post
. You would have to re-write the software in the HVAC panel (which isn't going to happen). But that's a moot point, as I think the real problem is as I described above (or possibly your car's A/C control module has gone bad).