Scott,
Any flat foam will work. (With flat foam the bucket will sit upright, with the handle under it, when it's back in the boat.) You could even slice up some pipe insulation type foam. Old winch strap or seat belt material works great for the handle material.
The bottom handle is the key to amazingly easy bucket retrieval.
Being a true yankee I understand about your reluctance to use a brand new bucket!
I'm glad the info helped you.

All the Best,

Gary