Not in a drawer, that’s for sure…
Whack a narrow rectangle from some random scrap of thin wood-like substance, squirt hot-melt glue along one edge, stick it to the floor joist over your tool chest, align it pretty much horizontally, take two deep breaths while the glue solidifies, then neatly affix your clamps.
Repeat as needed when you get more clamps: you can never have enough clamps!
The red-handled spring clamps on the far right hang from a row of nails where, this being directly in front of my tool cabinet, they don’t quite knock me on the head. I really wish the original owner of this house had sprung for one more course of concrete block; another nine inches of headroom would have been just ducky.
The Smell of Molten Projects in the Morning 
I know just what you mean about the low ceiling in the basement…along one stretch of mine, (1950 house) there’s a cold air return perpendicular to the joists. It’s about 6′ out from the long open wall, too. :(
Two more elbows and it’d be against the wall, but that’d be more time & materials for the guys doing the installation and nobody really uses that basement for anything, anyway, so why bother… [sigh]