OK, let's talk about "manual" shifting for a second ...

Assuming you have a repair stand, disconnect the cable completely. Now, crank the pedals.

On your derailleur, the parallelogram is the piece of the derailleur that says "Ultegra" on it. While you are cranking the pedals, grab the end of the parallelogram that is at the "U" end of "Ultegra". While grabbing that end, push the other end (the "a" end of "Ultegra"). By pushing on the "a" end, you should accomplish manual shifting by pushing the jockey wheels across the planes of each cog in succession. Until you can do the manual shifting, don't even both with the cable. It sounds like you could have a problem that's more basic than a cable tension problem.

You could do this without a repair stand by flipping the bike upside down and standing on your head. No, just kidding. Don't stand on your head ;-) But, crank the pedals and see if you can manually shift.