The Clausing sits on a steel box 21x21" x 24" high. Mine has the optional 4" riser block so it is 70" tall sitting on its box, but the standard is 66" tall. I had a similar issue with ceiling height, and my wife wasn't open to the idea of cutting a hole in the kitchen floor so I could get a bigger mill in there. It seems like most of the mills put the motor above the head, greatly increasing the height.
Grizzly sells a base for its mill / drills that is very similar to the style of the Clausing's base, but the dimensions are a different 18x28 x 24"H so longer but narrower. It is $325 so you could make something for a lot less but might be of interest from a design point of view.
Mill drill base
I was thinking a well built underbody truck box might be an option, if you could find a used one within your budget.
Something like this. The cheap ones are tin foil, but some of the ones I see used on semi-trucks are built with probably 16 or 18 gauge and are pretty solid.
Truck box