Understanding STREAM expression and Compression

You should be able to attach the compression profile and can remove the 'HTTP::header remove Accept-Encoding' from the iRule

https://support.f5.com/csp/article/K15434

"When you configure an HTTP Compression profile and assign it to a virtual server, the BIG-IP system reads the Accept-Encoding header of a client request and determines what content encoding method the client prefers. The BIG-IP system then removes the Accept-Encoding header from the request and passes the request to the server. Upon receiving the server response, the BIG-IP system inserts the Content-Encoding header, specifying either the gzip or deflate based on the compression method that the client specifies in the Accept-Encoding header."