I didn't actually need the hard hat itself for this project -- what I needed was the removable liner that comes with it. So take out the liner and do something else with the hat. Maybe save it for that Shoveler costume
you always wanted to do.
What's going on here is that you need to adapt the helmet liner to the up-turned bowl. Use your best guess and/or eyeball it to cut four small scraps of wood, sized to center the liner in the bowl. Also, make sure you have as much clearance as possible between the top of your head and the motor! This probably means placing the liner as low on the bowl as possible.
Experiment with the proper size of the blocks and their attachment points on the inside of the bowl. Use hot glue to temporarily attach them without having to commit to a screw hole on the bowl until you get it the way you want.
We're going to attach the wood blocks with screws. Drill a pilot hole on each side of the block so you don't split the wood (third picture).
For each block, attach it to a liner support (the parts that would snap into the hard hat if we still had it) with a screw (fourth picture).
The last picture shows all the spacer blocks installed. Attach them to the bowl with screws.