I figured i would use wire, chains, etc like you used to mount it. Vertically might be tricky but I am sure I could think of something.
I saw another thread this morning where guy made a nice stainless looking hood but used the silver colored insulation from HD/Lowes. Seems like a good surface to wipe dry and evaporate off.
My original plan was to do exactly what you did. build a box. But the rubbermaid tote or even this insulation idea sounds good enough for my needs and the people that tried them seem to have good results. I have a baby and anything I can do to save time or money is helpful.
Here is what i was thinking with the 2 possible fan mount locations.
I am not good at drawing a backwards bending tube hahah but the hole over the spray foamed rim joists is where the hole would be cut for the exhaust. I just can't get the fan up in the rim joist so it cannot be mounted right at the outlet horizontally. It has to be earlier in the exhaust system.