Basic idea:
Controlled by flight computer, consists of pump (gas compressor), and container for compressed helium
A little before reaching burst altitude (i.e. apogee), compress the helium, moving it from the balloon to a container; compress until helium is dense enough so that it no longer provides lift (no need to make as dense as air; payload weight will mean we can compress by about 3 times and stop lift).
Balloon begins to drop. At a chosen perigee, open a valve from the container, allowing the helium back into the balloon, thus increasing its volume and decreasing its density, so that it provides lift again.
Cycle restarts when apogee is reached again; this can continue indefinitely to keep payload buoyant at high altitude.
Could use solar panels to power pumps, this would allow the payload to be indefinitely 'parked' at the edge of space.
Give or take 1 km, this is effectively neutral buoyancy at high altitude.
Might not work, just an idea. Borne out of an idea for reusing helium, could also be used for this purpose by ignoring the action at perigee (i.e. just compress helium at apogee, let it drop back to Earth with parachute, and decompress helium on landing and store for reuse on a later mission). Initial idea from jatkins, idea of compression from edmoore/jcoxon (think it was one of you guys, can't remember). Would be great to discuss on the irc if anyone has any queries or suggestions about it.