Did you ever use the stripping powders (reducer) back in the heavy carpet dying days? Cobb carpet supply sells it, Its cheap, white powder very stinky, but I would mix it in squirt bottles very tiny amount fill with hot water and squirt, start job and just keep checking it and spray more if need be, by the time you get to that room the stains usually would be gone, You can get into a lot of trouble with straight reducers until you learn how much to use but if you do a lot of rentals you get the chance every day to use and practice.I use red relief by pros choice and have used this for 15 years without a problem
I will say I am not suggesting for anyone to use this at a house until you learn how to use the stuff but when you do learn it, its fast and very efficient. Ive been using this stuff since I was 18 before any of the red stain removers were on the market, hell I remember having to mix dye colors together to get the colors you wanted.
With the new poly plastic carpets today, the reducers usually take the red stains out on contact.
Learn the chemicals, what they do and don't do !