Hey, not going to give you second job advice but I was in your shoes back in the mid 2000s. I worked at a hospital and my boss gave me the unofficial "assistant lead" title and said I'd be promoted to lead when there was an opening, then the general manager a few years later when she was ready to retire.

Long story short I got laid off 2 years later and none of that panned out. Promises are great but worthless unless you get it in writing. Not saying this will happen to you, but it could.