Power steering fluid in master cylinder

okay bonehead dumb move. I siphoned out some of the brake fluid out of my reservoir. ( actually just used a sponge as I did not have a baster handy) and then refilled it with power steering fluid. by accident. ( dark. bottle looked same etc. I know dumb ) Just realized in now after 3000 miles of primarily highway driving as the brakes started to experience severe fade suddenly. Car is a 2002 Grand Marquis. So my question is . Since the brake hydraulics are a deadhead system can I get by with a replacement of the master cylinder and a reverse flush with alcohol and brake fluid. ( note I said reverse flush) and see what happens. I understand I may need to replace everything if that does not work. ( cost of $300 vs about $2500 for all new calipers, hoses… etc etc etc… ) Would the power steering fluid have gotten that far in the system? Note in the meantime I had the steering gearbox and midshaft replaced before I realized I had added the wrong fluid. would that have dislodged some of the fluid. any help would be appreciated.

Anti-lock brakes, right?? That system pumps the fluid into an accumulator with an electric high-pressure pump…The calipers MAY have escaped (and maybe not) but the master and the ABS unit are junk…