the best solution to being 'stuck in a department' is to expand outwards rather than upwards, speaking from personal experience, i haven't held nearly any senior cl4 roles (other than o1 major ages ago) prior to site admin, but have fairly valuable experience as i've tried a wide range of roles on the server.
while combat or non combat isnt everyone's favorite, it can still be great to try out different departments and maybe even get cl4 in it, a wide range of experience across multiple sectors will always be more valuable than extensive experience in one department.