From my post #12 - "And as others have stated, I'm betting on a buildup of debris in the trap and pipe that is limiting flow through your drain."
My response in post #12 of, "If your standpipe is 1 1/2", and as you "would occasionally back up when using different cycles", your best solution would be to install a laundry tub sink.", was in response the OP's comments in #9 and #11. They said that they had a "professional evaluation" done and they were thinking a laundry tub would be their "next best short-term idea". My comment was meant to suggest an easier way to install the laundry tub rather than using a floor cleanout. A laundry sink is actually a great selling point for a home and is an easy way to "filter" the wash water before it goes into the drain line.
But Twowaxhack, you are totally correct. The "professional" who evaluated the situation may not have truly "evaluated" the situation properly. And professionally cleaning the line, by someone other than the professional who was there before I would suggest, may very well resolve the issue. And it may even eliminate the problem of the occasional overflow during some of the machine cycles that have occurred from day one.
I do wonder if the OP knows that piping size is measured by the internal diameter rather than the outside diameter.