The reason that doesn't work is that you're explicitly overriding the right click button with the Mouse Button Control options. This disables the "Drag within groups" option.
You're saying that the issue was introduced in v4.5.4, but the behavior exists at least since v4.5.

A duplicate of http://tweaker.userecho.com/topic/517022

I cannot reproduce it, works for me on Windows 7.
Please provide your 7+ Taskbar Tweaker options and your taskbar properties, so I could try and reproduce it with your settings.

Please try the most recent beta version.

Implemented as an advanced option in v4.5.4.2 beta.

Please see my reply here:
http://rammichael.com/7-taskbar-tweaker/comment-pa...

Hmm, seems like you're right, I fixed "Switch to", but not "Minimize".
Please try the most recent beta.

I believe that I could reproduce and fix the issue.
Please try the new beta version.