"...when replacing the diaphragm, you need to find the correct balance of looseness, razz and tension. The balance that will enable your hum to grow and express itself. This is a process of trial and (often much) error, resulting in the sort of quest you describe..."

Membranes to try:

• "...normal kitchen grade wax paper - about 5 cm square. Crumple it to oblivion and the straighten it out again in a more or less smooth sheet. Take the sheet and stuff it into the sound hole of the kazoo so that it is not taught but sinks below the rim by about the distance of a thumbprint. Then tighten up the collar and hum. If it does not resonate enough, slacken the collar and press it down a tiny bit more. If it doesn't resonate at all it might be too loose..."
• Saran wrap
• Crumpled bond paper

WEBSITE: http://kazoologist.org/membranes.html