Take out the broken back half, wind the very BACK end of the outside end of the rod (opposite end to break) with some masking (or similar) tape (just a few fine turns, wound on VERY tight). Wind the tape from the "front" (old very back) of the batten back down the rod towards the remain tube section and (important) with the very first turn shape a small "point" with an overlap of tape beyond the end of the rod; this you can then twist down to help form the "arrow" you are going to use to direct the tape/rod/batten into the back of the broken rod.
then feed the broken batten back into the batten pocket BACKWARDs
(so tail/ rod/ tape first). Two people is definitely best now but not essential. Take some fine long nosed pliers (or Leatherman etc) and carefully push the (new back/broken) end of the batten so it goes all the way into the back end of the front broken piece.
Now the tricky part : using the long nose pliers carefully (you will be just INSIDE) the back end of the batten pocket at this stage ) twist the back batten around (like a corkscrew) and use the twisting to drive the taped end of the rod into the (broken) back end of the front tube section. At this time you might need a couple of tries to get the right tuning, adjust the tape thickness (more or less as required) and another hint to it try and work in the same twisting direction as the tape is wound on, so the friction against the front batten section tends to tighen the winding of the tape, rather than unpeel it.
You need to drive the back end of the batten fairly hard forward into the broken front pice, go carefully and again two people make it easier initially. But once you successfully docked and the tape grabs tight, you can withdraw the back half with the front half attached.
No damage to the sail required.
This all sounds wayyy complex (to write) but hopefully you undertsand the concept, with a little practice or experiment it works really well, especially if minimal other tools etc on hand. Another trick can be to use an alternate (longer) batten in the same way (either a longer one from that sail, or from another larger sail etc), but in most cases with a little practice the tape + reversed old back (broken) half is working fine..
I agree breaking battens is not fun, but especially in hi speed the impacts are pretty fierce and the super stiff tubes giving such good on water performance in these conditions do tend to become victims to 100kg projectiles hitting them at warp speed.
Cheers ~ Ian
PS : The repaired batten you did will work OK but obviously not technically as stiff at that point as original (rod joint being softer than tube). My best GPSSS this year I sailed the whole session with completely broken batten, cant be all bad..