The fact that your DS is unhappy is the real cause for concern. It is important to get to all the underlying factors.

You don't need the gifted coordinator's permission to recommend your DS for gifted. If there is a looming deadline, then you should just do it.

It is also important to remember that kindergarteners are really all over the place in acadmeic achievements at this point and there will be many changes through the year. This is relevant because it makes it that much harder for teachers to differentiate as well as makes them less inclined to do so.