Why do you say it is impossible? I think both your options you state are valid and common options. You can limit the lobby drop downs through the use of "Game Variants" which I'm sure there is a tutorial for in the link in my signature.
For simply disregarding the race dropdown in the lobby, I would hide it, using the "Player attributes" tab of Game Variants to set access to "hidden". Then use the trigger "Set Player Race" to set everyone to what you want.
I hope this was explained in a way that helps you, let me know if you want me to go further on part of this.