Actually, the problem seems to be that the gift cards cannot be used for deposit, prepayment, or pre-authorization, even though they should be usable as final payment at all properties participating in Marriott:
Q. Can a Marriott GiftCard / eGiftCard be used at any Marriott property?
A. Yes, Marriott GiftCards / eGiftCards can be used at all participating Marriott properties worldwide.
…
Q. Can I use a GiftCard / eGiftCard to guarantee room reservations?
A. No, a GiftCard / eGiftCard cannot be used to guarantee room reservations
Q. Can I use a GiftCard / eGiftCard to pre-pay for a room reservation (e.g. Advance Purchase Rates)?
A. No, a GiftCard / eGiftCard cannot be used to pre-pay for a room reservation
So (if the terms and FAQ are accurate) you need to supply a credit (or debit) card when you check in. The credit limit (or available balance) of that card will be reduced by your rate and estimated incidentals for 10+ days from checkin. However, the hotel should still accept the Marriott gift card as a form of payment at checkout.
I don't think there is anything you can do about your credit limit issue. That's just how the gift cards work.* (Also, you can't use the gift cards for prepaid (advance purchase) rates.)
(If you are not staying on a prepaid or advance purchase rate:) You should email
[email protected] to confirm that the hotel(s) you are staying at accepts Marriott gift cards. You should insist on paying with the gift card at checkout. If the hotel refuses to accept the gift card, you should ask them to confirm on hotel stationery that they refuse to accept Marriott gift cards, and then forward that information to
[email protected].
*My guess is that the gift card supplier has no way to do a “hold” on a gift card. If someone checked into hotel A with a gift card, and then spent all the money on it at hotel B's restaurant, then hotel A would be stuck without a guarantee from the guest. So the hotels put their hold on the credit limit on a real credit card instead.
If you have time, please let us know what happened, and which hotels these were!