I think I've heard of UK doctor's doing this. Okay, since you know this is your choice and have acknowledged that to be the case, if I were given the same option I would start straight away with estrogen.
I started with spiro and no E, my body and brain thanked me by ramping up the anxiety hard core for about two weeks (please someone shoot me levels of anxiety). I don't know why...
Progesterone will have a similar effect, it will nail your levels of sex hormone to the floor, and you may be able to handle that by itself, but it is a powerfully effective depressant as well. I figure you're eager to have this under way in the most effective way possible, and I understand, but your chemistry is about to change, and I'm sure you will notice very soon with either method.