Harrier and dschreib are exactly right for one of the problems. It all hinges on NOT selecting "Simplified AMT Calculation" when going through the interview, deleting the 1116 form when asked (don't worry, another one is instantly created), and answering a number of questions. Then, magically, a country (RIC in my case) appears in the 1116 AMT form. And the e-filing then goes right through. The interview does say that you must use the simplified method if you've used it in the past, or get a letter from the IRS saying otherwise, but ignoring that injunction I'm guessing is worth the risk for most of us. The only change on the 1116 form, the 1116 AMT form and the worksheet is the addition of the country name on the 1116 AMT form.
