I am surprised that your store was allowed to put Starbucks with anything other than Market. The company was pretty specific about keeping food areas together. You will need more time in Starbucks to get yourself and your team properly trained.
First of all, are you getting your allocated hours for Starbucks? If not, start asking that you get all of the hours you are supposed to have. Explain to your leaders that they need to invest in your training up front if you are going to be able to run a successful store. Maybe call your ETL over when you are working alone, and have him work register for 30 minutes. He may then get an idea of how much there is to learn.
Recruit and cross train. Even in a well established, well run, successful Starbucks, the team is always a bit on the outside. You will need to build a Team that is self sufficient and works well together. (By together I don't mean at the same time, but that they will support each other rather than complain about each other). About half of the baristas at my store also work other areas, so there is always backup available. It also helps them feel more part of the store. And, they can recommend tms who would be good baristas. In my experience, they really only recommend the ones they think will be a good fit, not just their friends. I am guessing that you are GSTL. We have all of our GSAs trained to at least cover breaks and backup.
Train. You should have 2 people besides yourself who can complete the order, MySupport issues, complete new sets, requisition, are certified trainers. Do you have anyone you think is up to this? We have a FSA as well who does most of the sets and ordering. Do you have a GSA you are developing? Maybe FSA for Starbucks would be a great step. It's a raise, and could be a good position to develop some leadership skills. Just remember that this is not a permanent solution, and that the goal is to move this person to the next level. Always try to have a back up person trained.
Your store seems to have chosen proximity to Starbucks as the reason for you getting it. This says to me that leadership expects you to spend time there, keeping your eye on things. Do this.
I realize that most of these solutions require more than 1 shift per week. I think you need to have a talk with your leadership where you present a plan for success in Starbucks that includes some more training time up front. Go in with a plan, not just complaints, you will get better results. It will be important to have Sbux running like a well oiled machine by Q4, so you can focus on FE.