Sorry to hear of your difficulties. Not sure what you can do with the current situation other than complain to the GM and threaten to withhold future business if they do not work with you. It does seem bizarre that they would not accept the gift cards, as they get paid just like they would with any other credit card.
The official T&C for Marriott gift cards state:
Marriott GiftCards may be used at participating JW Marriott®, EDITION℠, Autograph Collection®, Renaissance® Hotels, AC by Marriott℠, Marriott® Hotels & Resorts, Courtyard® by Marriott, Fairfield Inn & Suites® by Marriott, SpringHill Suites® by Marriott, Residence Inn® by Marriott, TownePlace Suites® by Marriott and Marriott Vacation Club℠ and participating hotel outlets: retail, spa, golf and food and beverage.
The key word in there, which I bolded, appears to be "participating".
For future stays, what I'd do in your position is email the hotel directly prior to booking to ask if they accept Marriott gift cards and e-gift cards. Get an email back, saying yes (from the hotel directly, preferably from a manager - you may have to call the hotel to get this person's direct email address) before you book. Then you should be on solid ground. If you had this issue again after confirming in writing, I think you'd have a good case for demanding a refund for the gift cards as they are not being accepted according to the published T&Cs.