Firstly, ask your ETL if you should be ignoring back up to the lanes, or endymes! Starbucks is no different. If they need backup, they need backup. Then, if you aren't getting all of the hours allocated to Starbucks, explain that you could stay in Market if your Starbucks team were getting all of their hours.
I think it is essential to have a great, reliable AST in Starbucks. Being a Sr, I was frequently scheduled only one or 2 days in Starbucks anyhow, so I had to develop a self sufficient group. I rarely do the order, and haven't for over a year. For the sets, we tag team them. Monday opener starts it (and sometimes finishes), and Tuesday opener takes care of whats left. I have 3 baristas I am comfortable with doing the sets by themselves. All of the baristas know how to date and put away the order. Obviously, this is not going to happen for you next week, but is something to work toward. You have to keep asking for both training hours and some offstage planning hours. If your ETL isn't fighting for you, try your ETL HR. I finally started getting my allocated hours for Starbucks when our new HR went to bat for us.
See if your receiver would be able to help out by putting the order into shopping carts for the baristas to push one by one.
Detrashing the mugs, etc. early helps on set day. Also having some of the signing assembled early is possible sometimes.
Try to involve your front end a little bit too. It is really helpful when GSTL/GSA can come over to take orders in a pinch.