I’m not an engineer and did not stay at a Holiday Inn Express, but I think I would use some kind of angle iron/brackets to support your channel with horizontal bolts to the joist, vs relying on a lag screw installed vertically
Also, use a bolt through the side of the channel, with a tube on the inside to prevent crushing it.
Can you install cleats temporarily on the wall, so that you can rest the vent hood on each one as you go up. The front can be supported by a couple of 2 x 4 stiff legs. With it balanced like that, one person can hold it, while the other installs the all thread, etc.
Edit: is there anyway to wall mount it? I saw in the instructions, they have a cleat that screws to the wall, but only holds 250 pounds.