It seems to have worked itself out in the past month.
When I started this thread, I was doing my kicks with an emphasis on trying to kick as hard as I can.
Since I've been more focused on the proper form, and not concerned with how hard my kicks are hitting the bag, my calf has been fine.
The best part is that my power is starting to increase while using proper form.
I've been concentrating on stretching my hip flexors a lot in the past 6 weeks, and my kicks have been much better as a result.
Insert profound martial arts quotes or tough guy phrases here.