Thanks to you for the conversation and guidance.
I finally got through to the St. James Health Department today after 5 phone calls where the person I need to talk to wasn't there. These calls will probably cost me about 30 bucks at $1.99/minute.
It looks like the only way to do this is to have someone on the Jamaica end pick up the permit. They will accept e-mailed death certificate and cremation certificate and generate the permit. BUT....they don't handle the payment. I asked about a USPS International Money Order, and they can't do that. The payment has to be made to the St. James Municipal Council. Googling this, I found St. James Municipal Corporation, which seems to be the same thing (http://www.stjamesmc.gov.jm/) at 19A Union St. in Montego Bay. They did not know if the council can accept an international money order, so I need to follow up on that. If they can, then all I have to do is find someone (Andre, as suggested?) to pick it up and there are no money issues.
If I could work out the money thing, and they could get a receipt from the council that the payment was made, they could e-mail me the permit. What remains to be seen is whether Customs would require the original, in which case we are back to square one.
Option #2 is to see if the hotel can handle this, i.e. charge the fee to my credit card and send someone, perhaps a driver dropping someone off, to pick it up. This might be the best option.
Anyway, there are further steps to follow. Logistically, it's still a crapshoot, because someone from my party would have to stay behind with the ashes until the permit can be brought to that person and who knows how difficult that will be.
I will have to talk to my sister and brother-in-law and see how willing they are to hassle with this. I'm starting to think these ashes may yet be buried in my backyard.