I do not have a good sugestion for you. The large volume of water from the washing machine coupled with a slow draining system, may force sewer gas back through a P-trap of a breakage in a pipe. You might have someone open the entrance end of the septic tank and watch the water flow when you do a load of clothes. If with this open, then perhaps you will not get the odor since there is another path for the gas to take. If the entrance baffle is broken, this could also have an impact. 

This probably has not helped much, but may be some ideas for you to try.