Only state government employers are going to have a governmental 457(b). Non-governmental 457(b) plans are subject to the creditors of the institution, limited to highly compensated employees, and often have limited withdrawal options (like say requiring 5 equal withdrawals over 5 years). They're also limited to non-profits, so no company will offer them.
Your best bet for all of those plans plus good investment options (less likely in public schools) is a state university or hospital affiliated with a state university.
My wife works for such an employer and has a 403(b) with mandatory contributions that don't count towards the salary deferral limit, a generous employer match, and after-tax contributions with in service conversion to Roth 403(b) (aka mega backdoor roth), and a 457(b). Altogether that's $73,500 of tax advantaged space. Throw in an HSA, a couple of IRAs and my solo 401(k) and we have access to well over $100k in tax advantaged space.