No, there's no way to automate it with 7+ Taskbar Tweaker.

If you're a programmer, you can come up with a solution by using the 7+ Taskbar Tweaking Library:

http://rammichael.com/7-taskbar-tweaking-library

There's the option to sort by name in Taskbar Inspector. It doesn't keep the windows automatically sorted, but that's better than nothing, I guess.

This issue exists only for the portable version, due to the syntax of the .ini file entries.

Yes, insider builds are not supported.

There's a post about this:

http://tweaker.userecho.com/topics/65-doesnt-work-on-insider-builds-of-windows-10/

Yes, insider builds are not supported.

There's a post about this:

http://tweaker.userecho.com/topics/65-doesnt-work-on-insider-builds-of-windows-10/

7+ Taskbar Tweaker is installed to the AppData folder by default. By doing so, it doesn't require administrator rights. Note that it's not portable: it uses the system registry.

If you prefer, you can run the installer as administrator, and install the tweaker into the Program Files folder by selecting it explicitly.

Like the sndvol_tooltip advanced option does?

Everything can be done. The question is, how much effort is required for it.

Currently, I don't plan to implement it, sorry.

I do not have 7+TT set to run on startup.

That's why it stops working, probably. The settings don't apply when the tweaker isn't running.