GIA is a good option, as is SSEF. Both use well defined x-ray views to examine an object. In this case, likely different views to determine the presence of a shell bead. In the absence of that, they'd look at the inner volume for the presence of grafted tissue, geometry of growth stages, foreign matter etc. Even then, they may rule inconclusive. This why candling in a home setting is a good thing as many times it tells you all you'll need to know.
Keeping in mind, it's exceedingly difficult to back-trace origin without provenance or sophisticated DNA tracking. A lab can generally determine species, but location not so much unless there are irrefutable exemplars in their possession. Pearls from identical locations can have unlike features. I'd expect both labs to have several of the SS variety. Even if they could name a locale, there are other factors needing to be ruled out (as opposed to confirming presence thereof). Keshi pearls tend to be smaller than their nucleated counterparts, but one can't say larger never happens either. A single oyster on a farm which was misplaced for a year or more (for example) could produce huge keshi pearls.
Like amber, I'd want to see the proverbial insect at the nucleus. I've seen numerous views of both pearl types across many species and locations. In the case of cultured pearls, the nuclei typically appear similar to one another, where in natural pearls they are almost always markedly different. Unique, even.