Well, I have finally done it. I finally have created a toe-up sock without gaps in the heel.
Want to know the secret? Well, I should have tried this years ago, but
Wendy has the best
Generic Toe-up Sock Pattern ever. It double wraps the short-row heel, and it works.
I would like to submit into evidence, Exhibit A: (a.k.a. gorgeous heel closeup)

In case you didn't quite catch that,
there are no gaps in the heels!!!!!
I have been trying to solve this problem for as long as I have been knitting socks. And man, am I glad to have found a solution. (And it's fun to do. Give it a shot!)
Hopefully I'll have made much more progress by the end of the week... the deadline for mailing out socks is rather close to my final exams...