Marty,
Cutting the comb isn’t a major issue, my comment would be to capture as much of the brood as possible regardless of orientation. I know some people comment about orientation but I haven’t had any issues with it in this situation. Basically figure out how best to get the brood to fit inside your Langstroth frames, and then include some honey stores (if they have some). The honey stores aren’t as important if you’re feeding immediately, so don’t kill yourself trying to get every last scrap.
There are multiple ways to approach it, this frame has two separate pieces cut side by side:
This one just has a large comb cut to fill as much of the frame as possible
The rubber bands are really there just to keep the comb vertical while they build it to the edge of the frame (the bees will do this surprisingly quickly). After a few days to a week you will find the rubber bands chewed up out the front of the hive, so don’t be too concerned about leaving them in there for a short while. The rubber band size doesn’t really matter, I always used thick rubber bands for strength, but as you likely saw the rubber bands from the last rescue were provided by the other beekeeper I was with and they were thin but worked just as well as the thick bands (you don’t need much strength in the bands to keep the comb upright).
One thing that isn’t shown in the above forum is that you can use a lot of rubber bands if you have smaller sections, and they can essentially make a ‘web’ around the frame if required to hold the pieces in… the bees will quickly stitch it all together.
As for the approach for establishing them in a NUC… I personally don’t do this. I would get their final destination (full size hive) and place the recovered frames in this. I always leave the hive at the original location for ~24 hours after moving the comb into it as you will find that a lot of bees disperse because of the disturbance and you will want as many bees as you can get. This one was left in the tree for about a week after relocating the natural hive into the Langstroth box.
Using the final box you plan to move to also means they don’t have to re-establish into a third home (it’s not just establishing comb… hive temperate/airflow etc.). I am saying all of this with the luxury of having a pile of spare hives in my shed, if all you currently have is a NUC box, then by all means use that 
As for foundationless frames, I personally don’t really agree with them, but I know it’s popular on this forum. When recovering a hive like this I always fill the box with frames of foundation and feed the bees to encourage them to draw the frames out to give the queen somewhere to lay. I generally place the recovered frames in the middle of the box and then frames with foundation on either side. In the below photo we used a NUC divider (essentially a follower board) to keep the hive small initially because we aren’t quite into Spring where I am)
I guess my last tip would be to try and locate the queen as early as possible in the process and get her on one of the relocated frames in the box as this will assist in encouraging the other bees into the box while you work on the comb.
If anyone reading this hasn’t seen the bee photograph thread link, the photos are from here:
http://www.canberrabees.com/bee-rescue/
hard thing to do starting up something like this from scratch with no background.
