I thought the way you did about mentoring others, and I love teaching. I think it could be worthwhile and rewarding doing DM, even if just for your own personal satisfaction, if you're as passionate as you sound. Plus you'll get a good taste of what it would be like as an instructor because you are going to learn the pro side of things, properly demonstrating skills, and managing divers.
I moved onto the IDC/IE primarily to have the freedom to teach as DMs are pretty much limited to teaching a few surface skills only. As an instructor, you could also independently teach - pick and choose the students, desired group size, and work with them however you want, and I know one person doing that quite successfully.
My non-internship DM course was conducted over 13 classroom / exam / pool skills / OW / dive leader sessions over a month of weekends and 1-2 evenings/week. Additional time was spent on the mapping project and lots of eLearning and knowledge reviews. I don't feel like an internship would have made the DM course any easier to complete.
The IDC was two weeks solid full-time, much more intense but the IE was easier than I expected. The IDC is where you will crash and burn the first few days with bad evaluations until things click into place, so the IE should be easy in comparison, even though all of us had anxiety and sleepless nights about it.
And I agree with marsh9077 - it's important to observe and work with good instructors to learn how they keep students moving, sequence all required skills in an efficient manner, and work the classroom/pool/open water logistics.