Didn't know... I totally get your point on syncing it!
Think because persona's are very specific, and may require lot of re-calculation based on the rules.
Available methods don't help a lot as the personainfoprovider
CMS.Personas.PersonaInfoProvider pip = new PersonaInfoProvider();
doesn't have a method to list persona data.
Using the PersonaService you'd be able to get the PersonaInfo object, but requires a dummy contact.
ContactInfo dummyContact = ContactInfoProvider.GetContactInfo("exampleContact@websites.com");
CMS.Personas.PersonaService ps = new PersonaService();
CMS.Personas.PersonaInfo pi = ps.GetPersonaForContact(dummyContact);
Which you would send to the 2nd instance and might be able to import,
CMS.Personas.PersonaInfo piCreate = new PersonaInfo()
{PersonaName = "abc",
PersonaDescription = "xyz"}; //etc
piCreate.Insert();
Where ect also should contains all the logic for the underlying rules... not to mention triggering the recalculation.
Which isn't ideal at all. I suggest to contact Kentico Support if they have any advise. Since I'm also interested please report your solution here!