Mist according to what the tub needs. Most tubs hold humidity very well so misting will probably not be needed often, if at all. You may even need to let the EcoEarth dry out some before using it in a sealed tub. I would get that set up so you can start testing the tub before you get a snake.
If you put the Eco Earth in the tub and you start getting moisture collecting on the sides or lid try letting the substrate dry out some then try again. You may find that it just holds to much moisture for tub use. I use ForestFloor cypress mulch, which is moist in the bag. When i set up a huge tub for my blood python's temporary home I had to let it dry out before putting the lid on because i had way to much humidity. I let it dry out and keep 55 to 67 humidity now. I think you would have a much easier time just using cypress mulch.
I have never tried using the temp gun on water but i guess that would work. I have a watch with a thermometer i use. I try to keep the water 80-85. I haven't soaked for awhile now. I started keeping moss in the hides and just mist it every few days.