How to select a text within the Highlighted text in Adobe Acrobat?
If you turn on the "Edit Text & Images" in the "Tools" panel in Adobe Acrobat, you should be able to select text inside highlighted region and right-click to do cut/copy/paste. I just tried on my laptop using Acrobat 11.0. Hope this can solve your problem. Not sure if Adobe Reader can do the same.
Some workaround for this very old bug.
Toggle Read Mode
On OS X: Ctrl-CMD-H
On windows: Ctrl-H
Use block selection
Shift + Alt + Drag-select