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?

I appreciate the information you've shared on this thread, @Deadwood Al.

I'd be delighted to address this solution you've shared about transferring funds between classes in QuickBooks Desktop (QBDT).

I agree with the details you've provided. Creating a credit memo for the amount referencing the class will move the funds out. Also, you can invoice the same customer you've used for the credit memo for the amount referencing the class you want the amount to transfer to. Thus, it moves the funds to another class if you don't retain the balance.

Moreover, you can also use a journal entry to ensure the debits equal credits for each class. But first, you'll need to create a clearing account. Then, you can make a journal entry like this in the visual sample reference below:

The fund is moved from the checking account for Class B to the checking for Class A. You can notice that each class has equal debits and credits. With this, you can also reach out to your accountant for further help to ensure the accuracy of your accounts. 

Additionally, this article can guide you in pulling up a balance sheet by class to see your balance sheet by fund, location, or other classes: What transactions are not supported by Balance Sheet by Class in QuickBooks Desktop?

I'll leave this handy resource here that contains a detailed guide to personalizing reports in QBDT about classes: Filter, sort, or total reports by Class.

You can always rely here in the Community space for additional assistance managing classes or funds. I'll be right there to help you whenever you need it.