This may seem counter-intuitive, but air in this case is the problem, so filling it less introduces more air (which is compressible) versus liquids which are generally incompressible.
But OP mentioned the bottles they use are not great so the problem they face may really be about getting better containers.
There at the end he revealed the point of the exercise; it wasn’t to have a functioning disk, but to push one’s individual skill boundaries and learn new ways to solve problems. If the disk worked at the end then it would be a double benefit, but that wasn’t the point.
It’s a lot like learning to fly or sail a boat. Are there more economical means of travel? Absolutely. But in doing these things we gain new tools to solve adjacent problems.
Do I have a need to finely and evenly spread a magnetic slurry? Nope. But the wire-wrapped rod may very well help me out in the future!
I studied Gaussian curves and found a mistress