Well, the tank doesn't itself have to be the superstructure or fuselage of the rocket. The tank can be a flexible internal enclosure inside the superstructure. Maybe it could be a flexible accordion type of structure, to ensure it contracts in one axial direction.
What about the evacuated space between the inside of your aero-shell and the outside of your flexible tank wall? Aero-shells need to be pressurised to maintain their shape and rigidity. What's going to keep your aero-shell from collapsing because of the pressure differential? Also, why would your flexible tank continue to passively shrink when there's an evacuated zone outside it? Any active system that performs mechanical work to squeeze the balloon is going to cost mass. What's that? You'd use Helium? Uhh....
Unless you want to think about entraining ambient air, that's what you'd probably converge on. But capturing ambient air would require you to siphon some off, and would cost you drag, shock, vibration, heating, and is still entrained mass that you're going to be carrying uphill. Not to mention the aerodynamic problems caused by the flow, when it encounters a possibly anisotropic shrinking tank.
In any case, I wasn't talking about the problems with the aerodynamic interactions as much as I was referring to the mass distribution upsets caused by the deviations in the contraction of the balloon; throwing the rocket off balance, and moving its centre of gravity around unpredictably. That would be a GNC nightmare.
Boron Nitride, by the way, has shown itself capable of forming a quasi-hexagonal mesh similar to that in Graphene and Carbon Nanotubes, but the BN structure is capable of buckling in an accordion-like manner, in a linear direction. That's one reason why BN nanotubes are being researched for tank armor, because this buckling characteristic offers energy-absorbing or damping properties. It seems like these intrinsic properties would still be available even at cryogenic temperatures.
That paper measures the change in the buckling behaviour of Boron nanotubes... when the nanotubes are subjected to an external compressional load. It says nothing about the direction of such buckling (accordion etc.), or the reversibility. This way.. you can buckle ANY material to shrink the volume, provided you ensure that it doesn't open up cracks that allow the LH2 out.
Plus, they're measuring the buckling in ISOLATED BN NANOtubes. Not BN Nanotubes packed so closely enough to form a seal impenetrable to Hydrogen molecules. But let's assume that a ring of BN nanotubes, spaced far enough apart to still exhibit the properties of nanotubes, rather than form a bulk solid structure -- i.e. stacked like the pillars of Stonehenge are still able to trap Hydrogen in the inner area because of a phenomenal adsorption power. Let's also assume that you can stack successive Stonehenges on atop the other to form a macroscopic cylinder -- or you're able to get a nanotube that's several metres in length; forgetting the difficulties of manufacturing a MULTI-STOREY structure out of NANO-tubes. (Boron Nitride btw -- atleast in the Wurtzite mineral form -- is harder than diamond and possibly the hardest substance known to man. Well...short of the exotic matter in stellar cores I guess).
For this structure to work as balloon tank, you'd have to ensure that the shrinkage happened only from top down... and that all your nano-tubes are aligned, and that it happens in the same direction, as opposed to the bottom half the tank shrinking down, and the top half shrinking up -- leading to a tear. You'd have to ensure this on a microscopic scale.
But...if you did all that though, I'll tell you one more thing you could do. You could get rid of all the wiring that needs to pass through that stage. The Boron Nitride nanotubes could act as fibre-optics!