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Been done and I hear it works well - the 308 cartridge has been necked up and down in every conceivable fashion. Of course it would require a custom reamer, guages and dies, but I appreciate the "just because" reason for wanting it. You could probably get away with using a set of 325 WSM dies for forming and neck sizing if you went to a 35 degree shoulder angle. Handloading would be a simple proposition - you could use 308 data (and a bit more due to the larger bore size).
If you wanted to use a military barrel, you'd have to trim and rethread the barrel (to shorten the chamber) - the 8mm-06 dosen't require that, so is much simpler and cheaper to do (and commercial dies exist for it). You'll want to base it on a short action receiver - a standard action gun (e.g. military) will work, but the mag will be too long and you'd likely want to modify the mag as well.