I have found that the tape that holds longest on my scalp is Walkers No Shine - up to 14 days. I have also found that the tape that adheres strongest and longest to lace for me at the back/nape is Duo Tac (mesh side) - more than 10 days.

To keep the back of the full cap down for extended periods I stick the Walkers on top of a long 5 inch boomerang strip of Duo Tac. Attach this combination to the cap and place on my head.

I can easily get more than a week with this, including sleeping everynight. I also use the No Shine tape (without the Duo Tac) across the partially exposed hairline and vertically down each temple/sideburn. I was on vacation in Melbourne last week and never touched the cap for 8 days.

Only downside is the two tapes on top of one another at the back is a little thicker, but my hair density is thickest at the back so anyone would really have to be digging in hard to feel it.