I got more legal advice from a lawyer based in Big City that is licensed to practice in both Country A and B. Turns out the differing advice H and I received from separate lawyers in Country B only give part of the picture; they didn't consider how to ensure that a divorce in Country B would be recognized by Country A, where we married. This "paperwork" is going to be a huge PITA.
After feeling hurt by H's pressure to get the divorce going, I now want it done quickly, too. I don't want any more of our marital $ supporting H's adultery.