This may be a stupid question, but are you looking at this from the wrong angle? Why do you need all three colonies to have equal access to all materials? Could you specialize each colony so it only consumes the minerals it produces, then move the end product around?
For instance, instead of each colony producing mines, construction factories and research labs, could you have one just produce mines, one just factories, one just labs and then move the finished installations around?
Of course you'd probably need duranium on every colony, but IMHO that is such a given that I'd have to think very carefully before starting a major colony in a system without any duranium resources available.
And this wouldn't work for shipbuilding, but that probably happens in a single central location anyway, I imagine?