You’re basically looking for three things that don’t always line up:
True privacy
Short-ish travel from the US
Adults only + food flexibility
That narrows it fast.
First, on Thatch Caye: the family style single dish per meal would make me nervous too if you both have real dietary restrictions. “You’ll be okay” isn’t the reassurance I’d want for a honeymoon. Smaller resorts can be amazing, but they also have limited kitchen flexibility. If food is important and allergies are involved, I’d be cautious unless they give you something very clear in writing.
Now for alternatives that are easier from EWR and more private than Sandals:
1. Palafitos at El Dorado Maroma (Mexico, adults only)
Probably the easiest travel wise. Direct flights to Cancun. The overwater bungalows are more spaced than Sandals and you get full access to multiple restaurants, not just one set menu situation. Much better if you need menu flexibility.
2. Aruba Ocean Villas (adults only)
More boutique, quieter vibe. Not a mega all inclusive feel. Aruba is easy from EWR and food customization is generally easier since you’re not stuck with one communal meal.
3. Jade Mountain (St. Lucia)
Not technically overwater, but insanely private open wall suites with private infinity pools. Adults only vibe even if not formally branded that way. Shorter travel than South Pacific and way more secluded than Caribbean OTWs.
4. Maldives (hear me out)
It’s longer than Caribbean but still doable in under a day from EWR with one connection. WAY more privacy than Sandals. Many resorts are adults only or very quiet. And they are extremely used to dietary restrictions. This is where OTW privacy is done right.
If privacy is the #1 priority, Maldives wins. If travel time is the #1 priority, Mexico or St. Lucia wins.
Given you have 2 full weeks and flexible budget, I’d honestly consider splitting:
7 nights super secluded OTW + 5–7 nights somewhere with more food variety and activities.
Your honeymoon shouldn’t involve worrying whether dinner will be something you can eat.