Wow! No wonder you are having problems. You got by with the old washer because it did not dump water as fast as the new one, but your drain system is really all wrong. You have an S trap and no vent. I think the simplest way to straighten this out is to start from the bottom and work up. You need a P trap located near the floor and a vent pipe. To avoid another S trap, you must have a vent after the P trap and prior to the drain turning down again. In other words, you can't go down, up, and down again without a vent. The S trap you have would be a P trap is the "clean out" continued up as a vent. However, that still would be wrong, because the trap is too high in the standpipe. The standpipe should be higher as well. Then the washer drain hose should not be tightly connected to the standpipe. The hook end of the hose just should hang into the top of the stand pipe. I think you can fix this problem fairly easily.