Propulsion technology for cubesats and nanosatellites is in active development, but there are at least a few based on sound principles that are likely to be tested in the next few years. There are also a few time-tested thruster technologies used on hundreds of satellites now that could in principle be engineered to put in a cubesat.
Question: What would be the best way to design a (say) 3U cubesat, deployed from the ISS or similar altitude LEO vehicle, so that at least a 1U section of it could attain a heliocentric orbit with the highest possible aphelion (no longer bound to the Earth/Moon system) using current or near-future cubesat-comaptable propulsion technology?
If it's helpful for example, it could be assembled already in the microgravity environment of the ISS, and gently deployed from there, in order to save on structural mass that would have been needed to survive launch from earth. Parts could be 3D printed there as well. Budget for COTS-type items is large, and "the shelf" is a few years in the future to allow for things that are not quite ready yet but probably will be.
A clever use of the moon's gravity is of course both allowed and encouraged. I just ran across this answer, which links to this NASA page: http://stereo.gsfc.nasa.gov/orbit.shtml. The first video is a nice illustration of how handy the moon can be.
Here is a GIF made from the frames of that
The 'at least 1U' part should have some minimal power system so it can measure something to verify its aphelion distance, a starcam snapshot of a few planet positions, or just a measurement of the 1/r^2 drop in solar intensity, or something different.
If spin-stabilization helps, assume that the method of deployment can set the attitude (aim it) and spin it if needed.
If you assemble it on the ISS, it should be considered safe to assemble on the ISS. Otherwise you'll have to launch from Earth the old fashioned way.