Does shedding short hairs (approx. 1") over a period of several months usually indicate AGA? Or TE short cycling? Other things?

The length of the hairs that fall out is likely not related nor can it be used for a diagnosis. In general it would be best to have a comprehensive examination by a doctor (in person) if you are trying to find the cause for your hair loss.

In my opinion, you should be evaluated by a hair expert. They will take a good history, examination including pull test and develop a treatment plan. I think the simplest way to determine the the diagnosis in question, is to do a pull test while you are losing the hair. If your losing hair in areas that are not normally lost with genetic alopecia then you probably have recurrent telogen effluvium. Look particularly at the back of the neck and sides of the scalp. Hope this helps. Good luck.

This diagnosis should be made by a good dermatologist. There are tests called the pull test (look it up) to find out of you have TE