Thanks for the various comments. I am currently rethinking my double emerald strategy.

For simplicity in raising the question, I mentioned the plan of achieving AA EXP first and then attending to the other (e.g. BA) program later. However, for anyone else in this situation, I should probably clarify that the desirable strategy, of course, is to anticipate your future flights over the membership year(s) and to carefully select which flights get assigned to which program while making sure that you will attain EXP by the end of the calendar year. For example, if you have a first class ticket(s) including the two segments PHX-PHL (2072 miles) and SJU-DTW (1934 miles) and then both receive virtually the same EQP on AA but on BA, the former is deemed to be long haul (>2000 mi) and the second short haul. Furthermore AA’s booking classification puts the former as first class while the second (not being within the continental US) as business class, so while the former earns 180 BA tier points, the second earns only 40 tier points. Conclusion: if you are working toward a double emerald (or sapphire too for that matter), be sure to carefully consider which flights get assigned to which program.