I get the value of working for the govt; my mom did the same for the state of TX and I understand the benefits. I also understand the stress of dealing with the pandemic as a working parent myself. You aren't alone here.What I do right now for work is a hybrid field tech / Jr. Sys Admin. I've been pursuing Application Specialist and Systems Analyst among several positions. However, circling back to my Master's Degree in IS Management w/Project Management focus, I've also been trying to seek positions within my employer that have an emphasis in Project Management, known by my employer as Business Analyst and Staff Analyst. The hurdle for me though has always been HR's application process. Each time I apply for Business Analyst, I end up qualifying, but the pool of departments hiring for this position is so small that I seldom get a call even for interview. Staff Analyst has always been more difficult for me to qualify for, and mainly because they deal more on the budgeting side of things which I have no experience in, I qualified for a Staff Analyst Trainee. The next part is waiting to hear back from a department who is seeking to fill the position and interview for them, and hopefully, get picked up by this department where I've befriended the hiring manager . The downside to the "trainee" positions is that they have a probation period of 24mo instead of the standard 9mo. I'm confident I'll make it, but if for whatever reason I don't, I simply get bumped back to my current position I'm in now.
So your pay makes sense for your Jr SysAdmin type of position but it does sound like you are overeducated/qualified for that role and you recognize that.
1) Is there a way to build up your resume on the business/budgeting side without adding additional degrees (like an MBA)? Perhaps by volunteering on the financial side for your neighbhorhood HOA/non-profit/church/whatever?
Showing you can work the budgets/business side of any entity where the money isn't entirely your own would surely add to your CV.
Hell, even a side business would show that.
2) Since it sounds like your job advancement into the analyst/product mgmt position is also gated by the amount of positions available, would switching to a different beaurocracy (with more departments) be beneficial for you?