Are you using an insider build? Note that insider Windows 10 builds are not supported by 7+ Taskbar Tweaker.

taskbar tweak set to show labels always

What do you mean by that? Did you set it to always show labels for explorer, in Taskbar Inspector?

In general, if you could provide screenshots, or even a video that demonstrates the issue, it will help.

I tried to reproduce it, but wasn't able to see the issue.

I launched the Ragdoll Masters game, marked it as a game according to this article, and launched it several times. My taskbar stayed narrow all way long.

Please provide the necessary steps to reproduce the problem.

7+ Taskbar Tweaker does not, and probably will never support third party taskbar implementations. See the discussion here:

http://rammichael.com/7-taskbar-tweaker/comment-page-14#comment-2835

Note that starting with Windows 8, there is native multi-taskbar support in Windows, which is supported by the tweaker.

Build 16251 is an insider build, and it's not supported. Also, I see that you're using v5.3.0.3, so you should have gotten a warning message about the incompatibility. Haven't you received one?

Looks like something that is tricky to solve. I'm afraid that I'm not going to look at it in the near future.

As a workaround, you can use a tool which is able to save and restore the desktop icons layout. There are several such tools around the internet. There are even command line tools that I found, just Google for "save desktop icon layout, command line".

Here's a new video in another format, now with your settings:

https://vid.me/bb6rd

Still, I could not reproduce the issue.

I tried to reproduce the issue, but didn't succeed. A video of my attempt can be found here.

Also, you didn't answer my second bullet.

I'm not sure that I understand the issue from your description. It would be best if you could provide a video, or at least some screenshots.

my first column of icons on the left of the desktop get moved to the first column on the left of the right screen

Do the icons move to another monitor? That's usually means that the relevant windows move to that monitor as well. Does that happen?

In general, because the tweaker starts after the taskbar is already created, if the no_width_limit option is used, the tweaker shrinks the taskbar. Perhaps that has some side effect.

By the way, how come that you have open windows on startup? Usually, no applications are open upon Windows startup.