Also posted this in the AA forum's newbie lounge, with some additions here.

Thank you for all of the clarifications. I landed in CLT and had checked 3 bags, anticipating that one would need to be used possibly to transport the rum. Purchased 3 bottles of Bambarra, the official rum of Turks and Caicos; not much in the way or rum made there generally otherwise but this was everywhere, and locals claimed it was the best legitimate rum from around the area. No significant sugar cane production in T&C due to such sandy soils so they sourced sugar from elsewhere, but have been making their own expression of rum since 2008 at Bambarra. I got their Heritage rum, a 15 year super premium very limited production aged rum that costs twice what their Trouvadore rum goes for, which is their general high end stuff that is not limited production... but I digress. Apparently you cannot get this rum outside of the country, and the only way to get it to the US is to grab it at PLS and transport it.

Anyway, I used the Global Entry app and the GE queue line in CLT and was literally through in less than 30 seconds from the time I entered. The "line" was just a couple of people who did not have the app but did have GE. I was waved through to the officer since I had the app and photos, showed the officer everything including the declaration, and was immediately waved through. The total value of the bottles was $240, so I suppose he did not really care to bother with me holding things up, especially as he was the only agent on the GE side at the time. The general non-GE line was about 100 deep with 3 or 4 agents but was moving quickly, it appeared.

One of my checked bags had two large packing cubes in it. I picked my 3 bags up, pulled the packing cubes out, replaced them with the booze, and took the packing cubes along with me on my person as pretty backwoods looking carryons for my final flight. The checked bags arrived with no issue, and things went smoothly otherwise.

Thanks for the help, all - you have helped me to get a bottle of this for myself, one for a good friend who is into rums, and one for a gracious host who had me and a few others to a nice property in T&C on his dime.

Despite a decent amount of flying, this was the first time I had ever purchased anything like that at an airport or tried to transport from another country, so thanks for the input.

I will add that I did have to go through TSA again after coming through customs at CLT, so there would have been no way for me to transport the booze given size of the bottles at that point aside from going through the ticket counter again and trying to check bags with the booze in them there, mid-journey, just for the second flight.