I do think I predicted this
but good to see you have found the issue and are correcting it. I hope the carbon tube will be strong and sturdy enough for the job. In my experience it can be pretty bendy as well on longer lengths.
I'll also restate my earlier idea, support the rod on 2 locations and put a "runner" on it that can detach from LOHAN once she's got her loins suitably heated. This does mean the length of the rod will be limited to however long you can support it over.