one possibility is to move from the "privacy" angle and towards the fungibility angle. I.e., if you break it down, the fungibility of monero is dependent on its untraceability and unlinkability. So, for each existing transaction on the blockchain that you include in your ring signature, you are increasing the fungibility of that transaction. If you include 2 others transactions, then the strength of that transactions fungibility can be compromised if those 2 transactions are compromised, etc.
For instance, if you compare a transaction with 100 members in the ring signature to one with 2 members in the ring signature, which one theoretically is more fungible?
Granted, due to points raised elsewhere, using a term like "fungibility level" would just create more confusion.
Something with the word "depth" or "width" might work, because when you add members,
ooooh. How about something with embedding. Because when you add ring members, you are really just embedding your transaction in the blockchain. You are weaving. Enmeshing. Meshing.