Unorthodox scum trying to break in

My advice would be to take the role. I'm assuming it's a big city or county that runs a sizeable operating/reserves/bond proceeds type portfolio (for themselves or depending on the state/setup on behalf of others.. i.e. California counties who manage large pools of cash). Especially if you are part of an in-house investment team, that's valuable experience in learning how to manage short term, liquidity type assets along with an understanding of the specific state or local investment policy/code restraints. Since you mentioned debt deals - that's another plus should you become more familiar with how public entities invest, manage, etc. their overall debt profiles and investments - but sounds like you might have worked at an MA firm or similar at one point. 

Public finance is an underrated - see: underpaid relative to private sector focused folks - realm to build experience and have a career in. That's the easiest route for me to see from where you are. Either making a run at a municipal advisor depending on your debt experience/overall familiarity with the entity or a run at an investment manager who specializes in public sector clients. The latter could take a variety of roles depending on your preference - could be a PM or similar managing short term FI portfolios, could go the relationship manager route to leverage your knowledge/contacts to drive business, etc. etc. Certainly you could also parlay the investing experience to a liquidity manager or someone who manages cash/short term fixed income... i.e. on the large end, a federated or similar. 

On the public sector career side, there's certainly a trajectory for you - don't underestimate your age in all of this. By wall street IB standards you might be old, but in the public sector - might as well be 22 again. Seriously. This is a huge issue for governments across the board, especially municipalities. There's a significant talent drain as older professionals retire and younger ones would prefer the higher wages in the private sector. Thus there's a lot of opportunity in my view both where you are at and outside of that should you be successful. Another option for you is to go from entity to entity - a $5 billion ish dollar muni is no joke should you climb the ranks there. 

Anyway - happy to answer any other questions or be as helpful as I can be. I've got experience in this space, at least enough to try and help you out as you think through opportunities.