
The carbon rods do pop out reasonably easily on my tent.(I have strong fingers:-))
You can pop them out and stuff them anywhere suitable like in the pole bag and then crush your inner and outer tent to your hearts content.
You can probably even get some carbon rod (local hobby store etc or use some arrow shafts) and cut some new poles from it of a slightly shorter length to aid removal without sacrificing the height of the tent. You would have to make some kind of protection or stopper on the tip and base of each pole to avoid damaging the tent fabrics.
A couple of mm could make a big difference here.
I would also paint the poles flourecent or put flourecent tape on them so thay can be easily found when you drop them!