Oh bumer. Not to worry, a good excuse to upgrade!
But on a serious note, i broke my 2-4 graphite rod a little while back and my dad somehow magically fixed it and the repair hasn't let me down yet!
Perhaps with my rod being graphite, the process you would employ here might be a bit different, but in a nut shell, he basically used a 4cm or 5cm length of round, aluminium tube, almost the same diameter as the rod itself. I'm pretty sure the 2 ends of the rod fit quite snug into this piece of tubing and he basically used araldite glue to join them. Probably worth sanding either side of the brake spot to allow the glue to get a good grip between the rod pieces and the tubing band aid.
I'm not sure if this will work in your case, as my rod broke further down and not so close to the top. You might end up with the same sensitivity in the tip regardless if you employ the same method i have described or if you chose to make the rod shorter. The tubing option is bound to make your tip a little less flexy, perhaps you can choose a smaller piece, say 3 or 4cm.
Hope this all makes sense and helps you decide. Let me know if you need any clarification.