What is the correct order to both marinate and velvet the meat?
Be sure to look at this related question too: How does velveting work?

Serious Eats just kind of took this on. They added some nice flavor to the velveting marinade, and then sauced the chunks after cooking. Some kind of adaptation of that concept would probably work well for you.

I have done some small experimentation with adding flavors to the egg/cornstarch marinade, and so far I haven't had any problem. As long as you've got enough egg white and cornstarch to make a light batter, you can add other things for flavor. BTW, the flavor of the velveting recipe in the question I linked to is lovely.