If the issue you are experiencing is due to the rewriting then you should be able to temporarily turn this off for the entire site then test out the map page with the API on. If you are not able to get the map to display here then it would suggest that the rewrite rules are not a part of the problem, however if the map does display it would indicate that the rewrite rules are affecting the page with the map still.
If there is a problem with the rewrite rules then turning them on globally should get things working, if the problem is something else this test will let you know and we can pursue the issue further.