Good day, @MW2020.
Let me provide insight into recording and tracking grant money in QuickBooks Desktop.
Using the Liability method on recording and tracking the grants is correct. This way, you can track how much your employees need to pay and how much they pay.
Also, you can use the Asset accounts, in which every time you're employee pays, you can create a deposit to the asset so that the value reduces.
I'd suggest consulting your accountant to make sure the accuracy of your books and some accounting help.
I've provided these articles for future reference:
Feel free to visit us here in the Community if you have other questions. I'll be glad to help. Wishing you well.