Both women were perfectly happy with their half of the baby
Don't you have that a bit mixed up?
As I recall the real mother agreed to let the other woman have the whole baby rather than cut it in half.
Maybe by the same token, anyone who really cares about the artifact would allow others to analyze it.
Most universities have a policy whereby they would analyze the samples for free provided they get to collaborate on a research paper about them.
My lab is unfortunately not set up for radio-carbon dating but we could easily perform a very complete material analysis of this or any other artifact, using our range of mass spectrometers and nuclear activation analysis techniques.
We have a policy of working very cheaply for any research projects and completely free if we get to colaborate on any research papers generated from our results.