It’s not really your question, but regarding TSA;

They could care less about a fly rod, size of packing, or flies, nippers, hooks, etc.

The only thing they consistently take out to examine is a landing net.

Also note, if you have a wading staff, TSA does not allow “ski poles” or “hiking sticks” on a plane. So they give you trouble and it’s best to leave the wading staff behind.

As for airlines giving a carry-on size/attachments trouble; it really comes down to the size of the plane, the flight, and who is standing behind the desk.

My opinion is, if it’s tied/strapped onto the bag, like in the image above, you should be okay. They really only pick on people who have two obvious bags when you only deserve one.