If your pack has loops, daisy chain, Molle strapping, etc on outside, you can nest the lens hoods as you describe and just put them in a stuff sack which you then hang off a loop.
In the old days when lenses tended to have similar (smaller) filter sizes, you could get rubber fold-away lens hoods with a filter-type screw thread. These compacted to 1/2 inch tall, and came in two lengths ("standard" for 40-60 mm FF, "tele" for 85-135m FF angle of view. See "General" brand at B and H. The problem is, these are not ideal for wide angle lenses because they don't come in tulip design with cut-outs. Nowadays, the tulip type of hood could be manufactured in flexible form (silicone), but I don't see anyone doing it.
Someone or other sells a flag that attaches via elastic band to the lens barrel, should you want to have both hands free to use on the camera. If you have the Rogue flash accessory stuff on hand, try their little flag/bounce and see if that could work.