If the savings is substantial* then absolutely go for the GTY stateroom. Then as soon as it's assigned look to change to a better stateroom in the exact same category.
Note:
* Substantial means something different to every cruiser.
OP: why not get off the ship in Cozumel and Nassau? Both are easy exits and the port areas are safe and free. No need to spend a nickel. Watch the giant screen in Nassau,,sit in the grass and stare at the ships in port. listen to the drunks sing in Cozumel. Get whistled at for crossing the yellow line. Go above the water snorkeling. Sit and people watch. Free free free free.
Many staff have told us "Others are not liking that recently, you'd be better off picking something else". We have blindly followed their advise and order something else.
Items from menu found online.
Wedge or Caesar Stripped of most things.
GRILLED JUMBO ASPARAGUS
SAUTÉED MUSHROOMS
TRUFFLED FRENCH FRIES
SALTED BAKED POTATO
Wife hates the freestyle machine drinks.
I want a "new" car as a perk😄
Gold and Platinum - 1981 Yugo
Emerald - The Shaft
Diamond/Diamond Plus - 1986 K-Car
Pinnacle - 1992 Mitsubishi Galant
They frequently pre-showtime do an mini-bio interview with questions like the following: What's your favorite Royal ship?, What's your favorite cruise itinerary?, Boxers or briefs?, etc...
If her issue with attending is "stage fright", then no need to attend. Other than that, it's a pretty mundane. Walk up, while a few people clap, take a picture, get the heck off the stage.