Sorry, I didn't read everything in this thread, but the USPS quit using X-ray machines back in the late 1970's. That's ironically, or not, about the same time magnetic media was routinely shipped through the mail.
Now, if you send packages to sensitive areas, then the consignees receiving handlers may subject any package to any amount of scrutiny...equal to but not limited to X-Ray, Star Trek Tricoorder, or sonic screwdriver.
Eggs shipped regular USPS First Class/Priory mail will rarely...pretty much NEVER; get near an X-ray machine.
I put, "Do Not X-Ray" on my egg shipments, but that's just for show.
Always label hatching eggs as, "FRAGILE", "Live Hatching Eggs", "Live Embryos" or some parts of the same, because that triggers USPS protocols that should be implemented to ensure they get a bit above average treatment.
The more people between point A and point B, can screw things up, but a well packed shipment of properly labeled eggs should get to point B, rather safely.
Everyone's results may vary, but a pretty average result.