Hi JC,
First off, congratulations on your raise and promotion!
Yes, your new job is getting to be quite a handful. That's a good sign. It shows your career is growing beyond your original comfort zone.
And it's great that they're trusting you to handle all these knotty problems, like motivating people and dealing with other departments in the firm.
Peko, t0, kip and zer0netgain all gave very good advice. I'd just like to add one thing, if heaven forbid you get knocked back down to part-time (and for the sake of anyone else reading this).
It's much easier to get a new job when you already have one, even if it's part-time. Prospective employers do not like to see gaps in employment. So if for whatever reason, including not enough hours, you need to replace your job, go out and search while you're still in your original job. Only quit once you've gotten a firm offer (specifying your exact job, title, starting date and pay) - preferably in writing - from the new employer.
And once you quit, do it in style. Just writing a brief letter of resignation saying that you regret you need to leave the job for another one - don't necessarily say why - and what your last day will be. (Unless your employer's policies specifically say otherwise, you should give at least two weeks' notice.)
Once again, congratulations JC!