Idea: HTTP server module that appends a minimal amount of hidden random garbage data (as a comment or similar) to each response so no two responses have the same fingerprint.
user btown answered that elsewhere here in this thread:
"https://github.com/technion/mod_randpad (an Nginx module that injects padding as a comment into returned HTML documents) is likely the correct layer to add random padding; the performance hit would be negligible."