Well, I’ve had success with bleach and detergent, Barkeeper’s friend for lime deposits and Venom peroxibright. There are liquid oven cleaners which are not lye based and cut crud really well.
In general, I’d suggest spritzing the wall from down to up, then lathering it up with a soft brush. Rinse with your gekko or whatever you have, then if there are any discolored spots, spritz bleach to lighten them.
I just can’t see laying out a few thousand for vapor steam equipment when you already have heat and pressure.
I would be glad to loan you mine if you want to mess with one, though.