If they really are full to the brim as you say then you only really have three choices, but before we get to those choices can you not rebalance store frames between your hives assuming same site and same 'disease' status? Or are you saying both hives are stacked out? If stacked out options as I see it.
a) SAFE: let them be! so your build up will slow down a bit, big deal, keeping is for the long haul not short term gain. OK, so you run a v low risk of being the earliest swarming on record, ever, anywhere!
b) MIDDLING: keep them in the BB as they are but replce a couple of full frames of stores with drawn empty comb (alternative would be to remove, spin and replace same frames if no drawn available to you but unnecessarily complex), remember - the last thing they need at this time of year is undrawn foundation to play with.
c) STRETCHING: throw a pre-drawn super on above the QE and accept the risk of chilling - it is afterall still only late March. If its not pre-drawn then forget it!
Which do you fancy going for and why?