It happens on IE 11 too, and for multiple Nutaku titles. However, if you use a browser that can have separate windows and not just tabs, you can leave FKG on the top tab of one window and use another window to browse elsewhere and it'll run full speed.
But personally, I'd rather just rageclick for a few minutes, get the whole map done, and then go look at something else while stamina rebuilds...the risk of losing out on a garden to the expiration of a tiny four-minute window is too great when distracted by other things.