Kuma, great questions.
"I've noticed something about UOA's--they really don't account for the quality of the base stock, do they? I mean, they really don't tell us much about that. "
UOA's were never meant to show base oil quality. They were meant to track general oil quality and trend wear and attempt to avoid failures from that trending. VOA's and UOA's will not show you some of the latter developed ashless additives.
The use of Nucelar Magnetic Resonance, Advanced Spectroscopy, and other techiques are the only way to determine base oil type, hydrocarbon spectra, and base oil signatures. In addition, the average person would not be able to interpret the resulting charts. And a professional interpretation would be very expensive.
"If Amsoil just buys their base stocks from Mobil, then how can they brag about being the "1st in synetics?" Or do they buy the regular less refined oil from them and then resynthesize it into their own blend? Are you getting essentially the same base stock with Amsoil and Mobil 1?"
The first question is somewhat political and very historical, but if you examine the history of the development of synthetic lubicants, neither company can claim to be the first. It was Standard Oil that developed the first synthetic lubricants even before the Germans, with Union Carbide actually developing a synthetic oil during the war, but that oil was never marketed properly after. Amsoil, IMHO, CAN claim to be the first American API marketed synthetic with their 10W40 oil (a di-ester) in about the 1972-73 time frame. Mobil marketed a PAO only 5W20 in Europe in 1971-72 time frame, but didn't get to these shores until about 1974, after which it became a PAO/ester formulation.
Amsoil get's the majority of their PAO's from ExMo. Amsoil executives have often commented that Mobil is their friendly competitor, and for good reason.