I'd guess the way to go would be chemical additives to the plastics. You work out a few hundred of them that don't degrade the strength, and have manufacturers assign particular ratios to each batch of plastic manufactured and keep track of which lots have which ratios when they sell them, and you can probably get a system going where any given object can be narrowed down to a few possible stores that could have sold the plastic used to produce it, and you can get an investigation going from there. With a few hundred ingredients you can vary, you should have enough unique combinations to last until the end of time, and I'd guess altering the base plastic is more dedication than the vast majority of people will be able to muster (which is the main thing that keeps most gun regulations working, anyway, as far as I can tell). No oppression potential, since you'll only have after-the-fact tracking available if you can find the objects themselves (probably bullets more than guns, in this case), and no additional pressure on the consumer, except possibly to pay with some easily traced form of payment, such as a credit card.
Trying to regulate the information is a losing battle, and legally limiting access to the machines themselves is an imposition I'm not really willing to accept. Between the existence of shame as a social concept, and the potential for "By using this machine, you agree that we own all rights to any intellectual property used in the construction of any items you produce" sorts of agreements, I don't think it's a good road to go down.