On the burden to the channel of passing a nominal 1/8" (3mm). I have myself worried that, and put a sleeve on the cord to distribute the load more broadly. I've also done what you have: doubled --well actually trippled -- the cord by passing a spliced continuous loop back through. I suppose I should once every many nights look for signs of wear toward the center of the channel, where the load is highest.
Others have urged caution about the breaking strength of the line. Should you switch to the 3mm cord most of us are familiar with, Amsteel / Spectra and similar with breaking strength in excess of 1000lb, know that it is extremely self-slippery. So must of us would probably think that it is non-abrasive to a fabric channel it runs through, even though many would follow a different practice of tying or looping the strong cord around a knob made of the gathered end of hammock-bed fabric.
I agree with Knotty on this one. Each hang is different, but the wisdom here is worth it's weight in gold.
I'm using amsteel strait through the channel ends...... Been working great .
"What one Man can do, another can do!"