First off - what do you mean by "the cable is over stressed". Was it once easy to move and now it's sluggish? Is it difficult to make the FD just move using the gear lever or does it move to a certain point fine and then you can move it no more?
Here's the official Shimano compatibility matrix:
http://bike.shimano.com/publish/content/global_cycle/en/us/index/tech_support/tech_tips.download.-Par50lparsys-0025-downloadFile.html/01)%20Drivetrain%20Compatability%20Chart.pdf
Since you're running a compact chainset, you may be able to make it too work - you may not. The indexing for the lever may not be correct and will move the FD an incorrect distance. I'm guessing that this is more down to the installation of the new FD.
First thing to check is that the cage plates on the 6700 front mech aren't hitting the chainrings. You may need to adjust the height of the FD to get this. Shimano recommend a millimeter or two between the bottom of the outer cage plate and the chainring.
The second thing to check is the limit screws - and I think this is what is wrong. There are two screws on the top of the FD - adjust as required. See the link below.
Tech tips for up front...
http://bike.shimano.com/publish/content/global_cycle/en/us/index/tech_support/tech_tips.download.-Par50lparsys-0027-downloadFile.html/03)%20Front%20Derailleur%20Installation.pdf
If it seems as though the cable is hard to move and it's not at the limit, likely causes are:
- Bad cut in the outer cable - part of the metal casing is pressing on the inner wire - remove cable, cut cleanly and deburr.
- Cable routing is bad. Things like bends that are too tight, bottom bracket cable guides dirty, cables not properly in the BB guides, ends of the outer cable not correctly inserted into cable guides or brake levers.
- Dirt or "other stuff" in the outer cable that causes high friction. Clean or replace as required.
I've run a 7803 FD with 7800 STI levers on a double with no problems... so there's hope that the reverse combination should work.