Yes, exactly. A deep pan / tray would be perfect, because when it will start boiling it needs room, so it won't overflow. I would say that a pan that is at least 25 cm / 10 inches tall is the best choice. Yes, the sauce / water and tomato paste mixture needs to cover the sarmale but not like in soup. Just enough water level to boil.LOL, you did write a novel - but a fascinating one! Recipes that are new to someone have a much better chance of success with as many details as possible!
So would your pan be about 2 or 3 layers deep? And in the end, there would be lots of sauce but not swimming or drowning in liquid.
I honestly admit I doubt I will make them - but never say never! I am still copying/saving the recipe. So maybe one day...