Are you sure you are running your amp bridged? Unless it is a 4 channel amp, this wouldn't be recomended. A 2 channel amp bridged basically is taking the two channels and making them one. That creates only 1 channel, so your music essentially stops really playing in "stereo" and plays more like mono. Great for subs, horrible for front speakers. Front speakers need separation. Subs are mono and omni-directional anyways, so no need to make them stereo.
Also, if your installer bridged the amp, you are either pushing 2ohm output into the speakers, or 8ohm. Depending on how your installer wired the speakers. If they ran it as 8ohm, it would have a lot less output, and you wanting more output from the speaks, would keep upping the gains.... causing clipping.
If you are going to run 135wtts rms, you should upgrade your speaker wires to 16awg. BUT I do not think this is the problem that is causing the clipping. Clipping isn't caused by running too small a wire. Too small a wire wont be able to efficiently run all the power you are running without over heating....it can cause a melt down of the wire. But even 135 watts through the stock wire, isn't going to melt it down. You have to get a little bit more power than that.
Your clipping, I expect, is due to the HU, Cleansweep, and amp gains needing to be adjusted correctly. It takes time and patience to get these straight and your system running at full tilt CLEANLY without damaging anything. I have my other car's system running cleanly. It took me a week - two weeks to get everything tuned and straightened out in order to run it full tilt without damaging my equipment.
If you still have issues, try and get a hold of TurboCad....he used to compete in car audio SQ.