It would seem to me to be a relatively simple solution, but there may be things I just don't understand that would make this solution not something to try: You now have my disclaimer!

If you create (or already have) a generic / internal "customer" or "vendor" that never is used for external invoicing or payment, and a GL account for "AR/AP Clearing" that is used for both sides (debit & credit) of a transaction, I think you could

  1 - Create a credit memo for $200 referencing the class that has the funds you no longer need restricted (HVAC in your example). This should move the funds out of that class.

  2 - Simultaneously, do an invoice (to the same customer or vendor) for $200 referencing the class you want the $200 to go into. 

  ** this should generate an invoice / bill of zero but move the funds from one class to another.

QB Experts: would this not work? If not, why?