I have used spectra a lot in fishing for big tuna. I use spectra in the 130 to 200 lb range. You can get spectra in varying "strengths" from any larger fishing tackle suppliers. Some considerations: Spectra is "slippery" and can pull a knot easier than you would like. It does not stretch and if the "line" is moving, it will cut whatever it is moving across, much like a very very sharp razor. (The message here, definitely do not grab your lines if you lose tension. You could lose a lot more that the plane.) Most fishing knots rely on some "cement" to help hold the knot from slipping, but as pointed out, this can be a weak area in the attachment.
With fishing, I used hollow spectra which acts like the old toy "Chinese hand cuffs" where you placed your fingers in a hollow tube, one finger in each end, pull and the tube closed up as you pulled, locking your fingers in place. The hollow spectra does the same thing. To make a loop, simply insert the "tag" end of the spectra into the hollow spectra, pushing it into the hollow area a foot or more, forming a loop where the tag end entered the spectra. Great you say, you don't need any cement to hold you say...well that's the theory. I never tested to see if any slippage occurred each time the joint was tested. There may, or may not be any slippage. If there is any at all, you would be constantly changing your handle adjustments.
I have never flown an airplane with spectra, and don't plan to. Considering the safety issue with the "sharp" material and the knotting issue I just cannot see a clear advantage over the lines we currently use.