Hi Flipflop.
My fiancée & I did the TS trip to Peru last year and it was an incredible trip and if you decide to go for it you will not be disappointed. We also did the Amazon add on which if you can do as well is a must see.
We flew with LAN airlines last year so I cannot comment on Avianca but having done a number of JY holidays before as well as the TS holiday and all the airlines they have used both internationally and internally have always been fine.
If you are travelling as a single on the TS holiday I can say there were 7 singles on our trip to Peru and everyone mixed together really well.
One tip for Peru is that the TS holiday goes a lot higher than the JY one so take some electrolyte tablets with you to dissolve in water to help combat any effects of altitude sickness.
If you decide to go have a great time.
Cheers Keith.