Do you really give Uber that much credit?
I most definitely do. As linked above me, Uber admits they have a proprietary algorithm that determines what they "think" you'll pay, and it is unrelated to the actual cost of the fare they are paying the drivers. Uber is a primarily a software company, so I have no doubt they're capable of what OP is finding, and for tracking requests in a similar area. I think both rideshare apps can tell which one I open first (by seeing if the other is already running) before giving a quote.
But in the sense of 'what will someone pay', I would think the algorithm would absolutely take into account that someone with 'free money' from Amex is more likely to use Uber than Lyft, but it would be smarter to make it a few dollars more, not double as was happening to OP.
I will keep in mind the Google Maps tip, though!