No, Amsoil synthetic is a very good oil. In fact, I truly have used over the last 20 years the cheapest synthetic, in my area, often found at Walmart in ont Canada, it's shell nautilus. I have never blamed an engine failure on my oil, having survived 2 trips at Havasu in 90's weather, at 7700 rpm, and a long punishing track,(800 cc expert LTD) .
One of my racing buds uses Amsoil synthetic (800 cc, 200 psi, msd, 7650 rpm). He has an engine that can go through 2 or more seasons without an engine failure. Now keep in mind, we are on 40:1 premix, no oil pumps. Did your overheat beeper go off? Sure seems like a lean mixture cause, but for both of them, seems impossible.