I got the 7600A # using logic and the explore chart.
Consider my 5 points:

1. If you plan to switch to a dictator you want to stay monarch as long as possible to maximize building capabilities.

2. Batch exploring is the fastest way to expand your land in the fewest amount of turns pre 1920A; however, since there's a max population penalty in the beginning, it's actually better to spiral up in acres pre 1920A. (And to be more accurate the penalty is NOT based on acres reaching 1920A but rather 80% of population).

3. Before 1920A you receive 45A per turn up to apprx 40-45 turns which will get you to 3800A. From there you can either attack or batch explore again. It seems more logical to batch again, since the returns by attacking at 1900A-3800A would be rather small. (I don't understand the logic of attacking pre-3800A since most attacks take 2 turns and they typically give 90-100A which is about the same from exploring w/ no unit loss).

4. Remember- on express you can only hit once or you'll risk get flattened- so it seems like a better approach to save those 1 hits for when batch explore returns are too small to be efficient. (The Express server has a small population, so I believe it's better to save targets near the end of the set rather than for the beginning.)

5. Since Express has approx 1850-1900 turns, it seems illogical to use 506 turns to go from 7600A to 1520A. That only leaves one option to increase land after 7600A & that's through attacking.

Thus, @ 7600A, in my opinion, I believe is the appropriate time to switch from monarch to dictator on the EXPRESS server.