I believe this is why washer standpipes are now required to be 2". I've always thought expanding soap foam was the culprit.
In a rental, I wrapped the washer drain hose with a 2" wide strip of old innertube rubber until it was a pressure fit into the standpipe. Some duct tape for extra security and it held for several years.

seeing images of P traps, i see they are all the same shape.
There is no "deep" trap option.
I think a normal shaped P trap of 1.5" diameter will still work well.

In Canada, the same washers work off 1.5" traps all the time. When US code got upgraded to require 2" pipe for showers and for washer standpipes, it was to allow longer distances so builders could make larger spaces. Otherwise a lot more venting had to be provided. My writing this out does not mean I know for a fact why a change in Code got voted by the committee; I'm surmising. Indulge me as I repeat the following factoid: in Canada, the exact same washing machines all work without backing up. Now, think about this. In Canada, is the distance of the 1.5" trap arm small enough to work right, or do Canadians just happen to put less soap in their soap trays? I really REALLY think that suds are not the obstacle to overcome.

Yes, deep traps do exist and were used in this tract of homes.

Here is a link that might be useful: Traps