I'm not trying to put you off the Canaries as I spent 13 years living there and had some of the best times of my life. I lived and worked in Tenerife and Gran Canaria.
It's just that I think there are better places to visit if coming all the way from the US. Many years ago there were a lot of American visitors i the Canaries as it was an add on after visitin other parts of Spain. These days there are very few. The majority of tourists are Europeans. Also, be aware that the resorts in the Canaries are nothing like the Caribbean, they are extremely commercialised and over developed and have lost any Spanish atmosphere. In the main resorts you will find plenty of British, Irish, Dutch, German, Scandinavian etc....bars and restaurants, but will be hard pushed to find any good Spanish places.
Last year I went to Puglia in southern Italy in mid October and loved it. The weather was very good, about 25-30C during the day, but cooler at night. We stayed in Alberobello, which is very central and a World Heritage site. You could combine a visit with maybe, Rome or Naples. Sicily would also be warm at the beginning of October.
Morocco would also have good weather. Look at the possibility of staying in a Riad. There are loads of websites as they have become very popular. You could combine say, Marrakech with Essouaira and a visit to the Atlas mountains.
Southern Spain and Portugal would be quite warm at the beginning of October. You could visit Madrid and then have time somewhere like the Costa de la Luz and also visit Seville and Granada.
Another option a bit further afield would be Egypt. I went to Luxor last year and am going back again this year. You could have some time in Luxor visiting the sites and spend a week in one of the Red Sea resorts, t will be hot in October.
Now, I know you are looking for all inclusive resorts and you will only find them in Spain, Portugal and Egypt out of the places that I have mentioned, but why don't you have Half Board in a hotel and try some of the local restaurants. In Egypt I would only do BB as it is very cheap.
Hope this gives you some food for thought