Should http/2 header compression not take care of the JWT size to the point that would make this more work than it's worth?
I tried in this post to not talk about the "transport". Indeed JWTs can be used with HTTP/1.1, HTTP/2 or even SIP. Furthermore HPACK maybe disabled in some cases. Here is what the RFC 7541 (HPACK) says about Authorization header (https://tools.ietf.org/html/rfc7541#section-7.1.3):
"An encoder might also choose not to index values for header fields that are considered to be highly valuable or sensitive to recovery, such as the Cookie or Authorization header fields."