Do you intend for this rocket to be your one and only HPR for a while? If not, why not build another rocket for your L2? Something with a 54mm MMT so you can fly full J, K and baby L motors too.
There are a lot of valid reasons for using the same rocket for both certs, but most of the reasons I've heard of involve cost. I understand about cost limits, and if you are only going to fly your L2 so you can volunteer for RSO/LCO at your local field, that's great!
The flip side is if you intend to fly the full range of L2 motors, I would highly recommend building a true L2 rocket capable of at least J and K motors and use that for your cert. That way you'll have at least one rocket to put a variety of L2 motors in before you start building bigger and bigger rockets.
Take all this with a grain of salt. You have to consider your home flying field, waiver, budget, etc. No decision is wrong, it's your hobby and do it the way you want.