Geoff, your post prompted me to break out the camera and see what fits.
Here's the cut I made in the door skin to accommodate my 6 Gal Better Bottles. I also had to remove some of the inside door fixtures but that was trivial.
Here's a shot with an Ale Pail. About 1 3/8" clearance on the bottom but the top still hits the door skin so you'd probably want to completely remove it.
And finally a plain 5 Gal Bucket. This one I got from Lowes but I imagine it is similar in size to a Homer Bucket. This fit my setup with ease and had about 1 3/4" clearance at the bottom.
I also have what I think is a 7 gallon bucket with a beer & wine picture on it. The bottom fits with about 1/8" clearance but in order to accommodate the wider circumference at the top of the bucket, the door would have to have the skin removed and possibly a bit of the insulating foam removed.