Good idea to make possible speed games, but big discomfort because of very short limit. 3 minutes are not enough not only to think where to move units but are not enough even for to move all units.
Increasing time limit could be good, for example, to 5 minuts for 1-3 turns, to 10 minutes for 4-8 turns and to 15 minutes for 9-15 turns. Such time limit could let the game be comfort and interesting.