What does the random Application ID look like?
You can try win7appid to create a shortcut with a custom Application ID.

Hi,
First, thanks for the donation :)
As for the feature request: well, multiple taskbar buttons usually represent multiple windows, e.g. multiple open folders. Making a left click to minimize them all is not appropriate. As far as I know, newer Photoshop versions create a taskbar button for every tab, right? In such case, I guess the best I can suggest is to use the classic right click menu, which has the Minimize all windows item.

There's no much logic, it restores in a more or less random order.
I don't think the feature worth the effort, as normally explorer shouldn't crash at all.
A much better solution would be find the cause of your crashes.

Then there's no way I can diagnose/fix the issue.
FYI, there's no much risk as the tweaker doesn't touch system files, only it's own in the installation path.

It works fine here on Windows 7.
http://i.imgur.com/ZpmhP6J.png

I can't think of a reason for it to fail, as the changes from v4.1.5 are really minor.

Can you try to update manually, by downloading the setup from the website?

Fixed in v4.1.6.

Do you get any error message? Or is it just loading forever?
You might want to try Softpedia:
http://www.softpedia.com/get/Tweak/System-Tweak/7-Taskbar-Tweaker.shtml

Here's a test build which does what you requested:
https://dl.dropbox.com/s/mfs3gwwjtu6k8su/7ttt.rar?token_hash=AAHInjPXiF14YfF5Zat8ZIZcwwTmwbP9RWasCvpAYGkYuw&dl=1

You might want to try it out, and see how inconvenient it is (in my opinion, at least).

I don't know how it works in Linux, but here, it's either you click early and get the list, or you don't click early enough and have the thumbnails shown.

There's an add-on for Firefox which sets different App IDs for different profiles.
http://rammichael.com/7-taskbar-tweaker/comment-page-9#comment-1872