[SW Dweller]

My AHJ will allow 6' and still be legal to a vent. A lot of water goes out of a washer at times.
Will your local area allow you to use the washer as grey water and use it for watering plants/grass? That is what I did for my washer.

 

[SW Dweller]

Dish or clothes? Dish fine, clothes, have a cycle (mine does) where it back flushes the filter scree for each wash. All those particles could clog up your concept.
Why cant you use a P trap and extend the horizontal pipe.

2" is not a great vent, Clothes washer spit out a lot of water all at once. Venting is very important with large volumes of water.