This weight question got my wheels turning....SO! ... I'm taking a dive down the rabbit hole.
(How many metaphors can you cram into one introduction?)
I have used expanding foam over the years in a few of my boat restorations. For big volumes I would first stuff in bits and pieces of the pink foam board used for foundation insulation and then pour in the expanding stuff and “glue” it all into a solid chunk. But when thinking about floatation, what you really want is a very low-density material that will be structurally sound.
What if you first filled in the space with something like ping-pong balls and then poured in the expanding foam? I guess the first question to answer is will the ping-pong balls dissolve in the liquid foam solvent before it sets up. That would end that experiment. According to google tennis table balls are made from Acrylonitrile butadiene styrene. That would definitly dissolve in strong organic solvents ... I could not easily find the solvent used to carry the monomers for the polyurethane expanding foam... but old-school ping-pong balls were cellulose and you can still buy cellulose ping-pong balls.
If you are filling a BIG space, I think you could also use PVC ball pit balls... like the kind kids jump into for ball pits....but I would worry that the polyurethane foam would not stick to that as well. Maybe also worth a small scale experiment????
I’ve even imagined using small 12 oz PETE soda bottles as the gap filler. I know PETE is resistant to most solvents but the "stick" issue might still be a problem.
(It must be winter)