After submitting my application to the website multiple times without getting a call (despite re-tailoring my resume each attempt), I decided to walk into the store and ask for the team leader. I ended up speaking with the assistant team leader, who was happy to take down my information after I explained to him my qualifications and strong desire to work there. He was happy to answer whatever questions I had, and then I was told to wait a few days for their next hiring cycle. Unfortunately, it was during a particularly busy time of year, so I had to wait a while. I went in a few more times to ask about when they'd be taking applicants, and I was updated each time. Finally, I was asked to come in one day to interview with the same assistant team leader and one other person from prepared foods.
We largely went over my resume, which they liked because my then-current job used many of the skills that their department needed. They asked me a few standard interview questions, which I believe I answered to their satisfaction. Afterward, they moved me onto the second phase of the interview, which involved a conversation with another person whose title I couldn't remember.
I was asked mostly character-based questions, which I felt I did well with save for possibly one or two weak answers. The interviewer noted that I seemed very serious (which might have been a result of nerves from the interview process - I had really wanted this job!). The interviewer still seemed happy to have spoken to me. I then met the assistant team leader again, and was told that they had a few more candidates to sift through, but they'd get back to me before the end of the week. I was told that I'd have a final interview that involved various other heads of the store.
It ended up taking longer than that, and I once again returned to the store to ask if they were making any decisions yet; the assistant team leader again updated and took down my name and number.
Finally, after about a week and a half-later after the initial interview, I was called and offered the position. I apparently didn't have to do the final phase of the interview for whatever reason.
Strangely, during this entire process, I had never met or spoken with the actual team leader of the department.