oacdesigns

Don’t know if you’ve solved this by now, but for the tabs to show up in the admin page you need to first visit the page on the frontend so that the blocks can be initialised.

And now everything is broken

For example
<li></li>

[Please post code & markup between backticks or use the code button.]

I think I found a workaround solution to your problem, at least it solves it in the design I’m currently working on.
Set a negative left and right margin to the
<li> elements.
I’ve found the -0.125em will close the space.

Here’s a jsfiddle displaying it
https://jsfiddle.net/DigitalBiscuits/ftgfD/