As a night owl or a night person, how do you avoid feeling like you’re missing out on your most productive part of the day by not staying up and getting things done past 10pm?

You have to get back that time in the mornings. If you go to bed earlier then start waking up earlier and training yourself to do work in the morning. It does take a lot of time but you just got to be patient with yourself and let your body and mind adjust. Its a big change but you get extra time in the morning to do whatever you want.