Currently, you can do this with Taskbar Inspector: double click on the AppID, right click and choose to close the windows. Not super-quick, but as the action is not very frequent, I think that it's good enough.

Heh. I changed it to "The 7+ Taskbar Tweaker Team", before someone else starts wondering about my personal habits :)

A duplicate of:
http://tweaker.userecho.com/topic/604551-first-use-of-show-desktop-after-launch-7-taskbar-tweaker-with-enabled-disable_topmost-removes/

Thanks, but I'm not able to download the file. What I see is a page which is mostly blank.
Could you upload it to a different place, or email it to me?

Should be fixed in v4.5.8.3 beta.

Sounds similar to this issue:
https://tweaker.userecho.com/topic/270602-thumbnails-not-displaying/
Is that it?

having the tab arrive in a predictable position (say, near where it's dropped, or always at the end of the last row) after right-dragging the tab would be more useful

That's the intent, and it works pretty well for a single row, but for multiple rows it gets more complicated, especially when there are groups which span through multiple rows. How about dragging it to the upper left corner? Then it will end up being the first item.

Note: I understand about the Explorer thing where navigating folders causes the Explorer task/tab to jump out of chosen group and back to default Explorer.exe group.

Check out v4.5.8.2 beta ;)

With the Drag within/between groups using right mouse button option, dragging a button out of the taskbar will create a new group. Seems like that's what you're looking for.

I believe that the issue might have been the server load. In the last few hours, the server responsiveness was not ideal, probably due to all the users which try to update to the newly released version.
Anyway, I'm glad that you got it sorted.