We went to Beaches Negril this past August. Loved it! My teens had a ball but found their structured teen programs lacking. However they were SO busy during the day that they were wiped out at night anyway. Gorgeous property (small compared to Turks) excellent service and really good food. We all look forward to returning.
The EPIC on NCL - kids had an absolute blast! Their teen program was excellent. The only problem I found is they didn't want to hang out with us - at all.

Food was great and service was also.
Dreams La Romana in Dominican Republic - again a very strong teen program and offerings. They kept them going all day and night if they wanted to. Lots of scheduled options, a teens club and very welcoming staff. The staff rounded up all the teens and had many opportunities for them to socialize and have fun.
I've been researching too so cant wait to see what suggestions you get! I think we even talked about Beaches last year - our Turks trip got cancelled due to the hurricane but I was there once already.
We do lots of all inclusives but these are the few that stand out as most fun for the kids so far.
How about Atlantis? I hear they started an AI - going to look into that for us.
Also, Costa Rica Westin Playa Conchal.
Have a look at Iberostar properties - lots of fun, good service and teen programs. I know you said no Mexico but they have a great reputation there and elsewhere too.