Would it not be just easier to drill narrow deep holes and then pour resin in instead of a drill for an inch and then let it seep through...you can definitely see the absorption in the handle further than the 1inch cut out, looks like black specks on the cane.
Also since you are allowed 10% other materials in the handle why not use carbon fiber tape on the handle, over or under the twine? that would/should cover the entire handle and still could be legal!!
I doubt that resin alone would make a substantial difference to the properties, I think it would be needed to combine with something that has a higher tensile strength than the cane.
The carbon fibre /kevlar idea would be worth a try however.