Add a toilet to washing machine drain line

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.

What you are looking for is the Laundry-To-Landscape system: http://oasisdesign.net/greywater/laundry/

This system works very well and is easy to implement yourself at very low cost. I have implemented it myself and it works perfectly, providing much needed irrigation water to my parched desert yard (not a problem in Mississippi I imagine!). And unless you're washing poopy diapers, laundry is graywater, so it's not a health hazard. You could direct the water to mulched trees, or a gravel-filled trench you could dig. But don't just dump it onto the grass.