Is there anyway to fit a breadboard into a 1.5 inch wide space?
I haven't seen a push-in breadboard that small, but you could verify the circuit on one, and then use a generic solder-able breadboard for the final circuit. These can be found at any major supplier for very low cost. I am not sure how robust it would need to be for your model rocket application, but soldering the components in would likely hold up to vibration better than the push-in style breadboard.
Example:
Digikey / Sparkfun