Hate to be a wet blanket, but...
I think the best use of THAT rod would be as firewood. Once the glue starts to let loose, unless you want to take the "sticks" completely apart and start from scratch, carefully sanding to remove all traces of glue and varnish WITHOUT disturbing the taper, and start from scratch.
And if pieces are shortened, they PROBABLY will screw up the action.
I would also use new ferrules, instead of screwing around with the old.
There were MANY brands of bamboo rods, and the vast majority were cheap rods that sold originally for under $5. They have an "action" (if you can call it that) like a piece of very limp spaghetti.
There are only a handfull of "desireable" brands of rods. I'm not a snob on this, it's just a fact of life. Yes, a Leonard or a Thomas rod would be worth salvage. But unless you have the time AND THE KNOWLEDGE of how to "glue sticks", and the patience to wrap and hold them while drying, then clean up the resultant mess without ruining the taper, you're in for disappointment.
"Restoration" does not necessarily mean making something like new; it also means preserving the original work and maintaining its condition "as is". Antiques are worth more that way.
Sorry, but that's the way it is!