You need an emergency travel document. The people who should be getting you this is the American Consulate, and since there isn't one in Turks and Caicos, the Bahamian one should be responsible.
You seem to have taken a very relaxed attitude to this situation. When the action recommended by the Bahamas consulate didn't work, you should have immediately called them again, not waited seven months for a reopening that clearly won't happen. If you didn't do that, they will have assumed you got home successfully or don't really need to leave. Even now, if you don't call them frequently, they will assume that you are content with the current situation. They won't do anything unless you ask them.
You should call the Bahamas consulate every day or two until you get a resolution. Tell them it is urgent (although they may be skeptical since you seem to have been OK staying in the Turks and Caicos for seven months). Don't bother calling airlines, CBP, State department or TSA (unless the consulate tells you to).
Anything else you try, like trying to sneak into the Bahamas, is likely to be illegal and have repercussions down the road. However an option you could try is to apply for a replacement passport in the regular way and have it mailed to a friend in the US (they won't mail it abroad). Then have the friend bring it to you in the Turks and Caicos. This is likely to be tricky in times of Covid, but should be manageable.
Be aware that if you don't apply for a replacement passport soon, you may find that you have to apply for a new passport rather than a replacement, which will be harder.