Most of the questions asked here have been answered. A couple of things to mention. US airlines don’t pay overflight fees to fly in US airspace. The FAA airspace system is free. They do however tax the airlines left, right, backward and forward in other ways. Mostly that involves airport use fees, fuel taxes and passenger fees.
There is a FAA enroute facility in San Juan. They control a good chunk of Caribbean airspace. Not all of that airspace is under positive control as they don’t have radar coverage throughout the area. Much of it is done via position reports and estimates. SXM is under SJU control.
As far as the pilot shortage it’s a combination of many things but the main areas are a vastly reduced supply of military pilots, regional airline pay and a panicked reaction to covid by the airlines. On the military side most people are unaware of how much smaller our military is verses even 20 years ago. They are training a fraction of the pilots they once did. The percentage going to the airlines has not changed there just are far fewer to start with. The civilian pilot pipeline was crushed by airline managements in the 2000 to 2014 time frame. There was a surplus of pilots and airline managements took advantage of it in every way possible. Wages were so low that most regional copilots and some captains qualified for federal assistance programs like food stamps. Some airlines like the prior incarnation of Silver Airways had copilots flying for free trying to build hours. Low pay combined with horrid work rules led to a collapse of the civilian training pipeline. The final problem was the major airlines extreme covid panic. They all took federal bailout money meaning they could not furlough employees. Instead they offered very generous early out programs using tax payer money. Delta as a example let 1800 pilots retire early. They have not caught up today and still can’t fly the schedule they want. This is on top of a very large wave of normal retirements. The shortage is so acute that regional copilots who 10 years ago started at 18,000 a year now start at about 100,000 a year and get up to a 150,000 signing bonus. The old saying that you reap what you sow comes to mind. Management greed when they had a surplus is killing them now.
The pipeline for training pilots is still not rebuilt. Issues include a lack of instructors and training aircraft. Foreign airlines have locked up a significant portion of flight school slots in the US. Training aircraft are hard to acquire and US liability laws simply won’t allow new aircraft to be built at a reasonable cost. 50 year old Cessna 172’s that ten years ago sold for 25,000 now go for 100,000 and more. Flight school starts are way up and the pilot problem should ease but projections still show a shortage for at least 3 years and the regional side will probably never return to the number of aircraft they flew 5 years ago.