I’m new here and to playing harmonica, so aloha!
Part of what you’re doing is called “time blocking” and is defined by blocking out a fairly short amount of time and doing something, and doing it only for that long. (5 minutes, 15 minutes are the most common amounts). This is also sometimes called the “Pomodoro technique” because it was popularized in recent(-ish) years with a tomato-shaped timer used. ("pomodoro’ is Italian for tomato).
It’s a great technique for doing something you’re not keen to do (including things like cleaning 
or getting to things you’ve been procrastinating).
Because you know it’s relatively short and it is 100% OK to stop after that time, you can do it. (Works pretty well with kids and chores, too.)
Great to see/hear it applied to practicing a new technique!
When training dogs, I really learned the importance of (1) stopping before you’re frustrated (the dog or you), and (2) trying to always end on something fun and positive.
Setting a time-limit is a great way to help with (1).
I guess ending with something fun and positive might be to play whatever you’ve most recently accomplished/gained confidence with. For you, Luke, I guess that’d be to end with whatever arpeggio you feel great about. For me, it’d currently be a simple train chugging (v e e e r y . s l o o o w l y 
) One day it will be a consistent, solid sounding 2-draw.
I know the OP is old, but I’m reading through the forum (learning lots!) and thought I’d chime in.