I think the solution is to calculate staff salaries each season like players, but also make the staff trainable.
First, give them ages & five skills:
Doctor - Injury Reduction, Taping Injuries, Massage, Experience, Potential
Trainer - Skill Development, Fitness, Career Extension, Experience, Potential
PR-Manager - Marketing, National Appeal, Crowd Involvement, Experience, Potential
Then let teams invest directly in one of these "Professional Development" options each week:
- Injury Reduction Conference
- Training Conference
- Marketing Conference
- Injury Taping Seminar
- Fitness Seminar
- National Media Seminar
- Massage Clinic
- Skill Maintenance Clinic
- Cheerleading Clinic
Just like players, make young staff develop faster than old staff and make really old staff deteriorate.
Then, have a "HR Department" that has all the staff whom you could hire, including both a steady stream of new blood and the staff other teams have let go. The "HR Department" would be a TL for the staff, except everyone would be a free agent. Then all we need to do is base salaries on skill levels and experience, making older staff more expensive (someone has to pay into their pension funds!), and we have a functioning staff economy where you pay for what you get and have an incentive to change staff from time to time!
Additionally, there could be the random possibility that your staff might decide to leave, at which point they would spontaneously put themselves on the "HR Department" list (of course sending a notice to your "BB News" page so you could lure them back with a bonus). The desire to leave could even be a "hidden skill" that changes based on age, length of employment and success - like in RL.