I didn’t read through all the responses but definitell avoid the warm bath you mentioned. If I can’t dunk it in an ice cold stream, then when I get home it goes in the tub with ice water. Its much better for blood.
Exo just did a podcast on this. Soak it in ice cold water. That’ll draw the blood out.
Also, if you’re using a load shelf, put a contractor bag between your frame and the meat and between the meat and the bag. You can just use one bag and split it. That won’t keep all the blood off, but it’ll definitely lessen what you get on the bag and frame while still letting the meat breathe.