How can I stop my washing machine drain from overflowing?
It sounds like the pipe is partially blocked and water can only get through at a slower speed.  The drain at the hot water is the lowest point so that's why it is coming from there.  The blockage could be anything, from debris that came in through the pipe in the service closet or a sock that made it out of the washer.  Since it's after where the water is coming out of the service closet then you might be able to get a drain snake the problem but you might have to get an expert to get it cleaned out.