You will not damage your receiver with long runs, or skinny wire, or both. These tend to raise the impedance seen by the receiver - which it is perfectly happy with. In fact, if you had very low impedance speakers (say, below 4 ohms, which would normally cause a problem with the receiver) a long run of skinny wire might help the situation and keep the reciever happy

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The two things that will happen with long skinny wire are: 1. You waste some power in the wire -therefore giving up max volume and headroom. 2. You change the sonic characteristics of the speakers slightly because of the increased source impedance. Bass quality is usually the first to be affected since the impedance changes the system tuning.
Personally, in your situation, I wouldn't sweat it. Changing from 16ga to 12ga will reduce the wire resistance from 0.56 ohms to 0.22 ohms. Not likely to be audible with surround speakers. If you do decide to upgrade, there's nothing wrong with the PE wire. I used 12ga Home Depot speaker wire in my fairly high-end system (4KW total amplifier power). The runs to my rear surrounds are about 40'.