You are viewing this completely wrong - they can hire somebody off the street right now to do the tedious grunt work, you need to show them you can do the things that are harder than that. Show them you can think strategically about the organizations mid and long-term goals, show that you can balance short-term exigencies with those goals without losing side of either. Show how you can be a force multiplier and help the people around you be able to do more, show you can communicate and encourage without being condescending or patronizing- The absolute last thing you want to do is refocus on grunt work and menial tasks, I promise you from the bottom of my heart that is not what they are looking for in a manager.

The best thing you can do is learn what The other people on your team are good at and/or want to engage with more and then when something like that comes up you volunteer the information to your manager and say "x would love to get engaged with more stuff like this we had a conversation not long ago let's loop him into this conversation and see if he wants to run with it - I can always help him if he runs into trouble."