Does it say the entire rocket must use helicopter recovery? Or just the nose cone and payload. You might want to look at the Estes "Sky Twister" design. If i recall correctly it's a BT-56 based rocket, which is just every so slightly larger than Bt-55. Anyway, you should be able to fit a 29mm motor in that. If I'm not mistaken it separates into 2 pieces and the nose cones somes down under helicopter recovery while the launch vehicles come down on either a streamer or parachute. This is from memory. I had one back in the day, but I'm not totally sure now.
Also do the rules say the rocket must be entirely scratch built or can it be sort of a kit bash, where you use existing parts from kits to create a modified design? If the later is possible and it were me, I'd pick up a sky twister and modify it to suit my needs. If you only have a month, this might be a wiser choice that reinventing the wheel.