Cannot comment on your Grand Mayan timeshare. But definitely list it on TUG. I have sold 2 timeshare on TUG, one about 3 years ago, and the 2nd one a week ago, and interest in a 3rd, which I just pulled when we decided not to sell. The 3rd is a Marriott, which Marriott resales department indicated that it is waitlisted and the ones listed are not moving. Marriott indicated that if I want I can deed it back, which is not my desire. We will continue to use it for a while.
Be realistic on the pricing if you want to sell, and then be patient. Continue to check and compare your competition in TUG, Redweek and other sites to make sure you are not pricing too high. I painfully dropped the price on my 2nd listing because I got impatient. Then I got 3 separate offers last week. I could have gotten more but I just wanted to move on.