You should consider calling in, because the website results are incomplete (not all carriers permit it). And who knows, maybe a different routing option is available if you feed flight numbers to the phone rep?
I have called before and been given the same price as Google Flights, so maybe your dates/routes were just lucky?
I will though take to heart the advice to read carefully if Amex is willing to mix fares like that. I have less trust in AmexTravel.com (aka Expedia) than I do in Platinum Travel Services and have considered going back to the $39 fee in the future for peace of mind.