I don't think there's enough depth in the adjuster to get the length you need and still support the back of the batten . I would be thinking of cutting the batten about a foot from the back and gluing in a solid pin , ( alloy rod, thinner batten or something like that ), extending the cut the 3 cm that you need. Make the pin around 20 cm long . The back part of the batten doesn't bend , so solid if fine.
ps, pre measure the total batten length with the broken bits . Clean up the broken tip . Take off the plastic tip of the broken part and glue it to the new tip. Measure length of batten. Now you will know exactly how much gap you will need in the repair . Rough up the repair pin a lot and clean the inside of the batten. It doesn't need to be a super tight fit . Araldyte glue will work fine it it's a wobbly fit , superglue if it's tight . First glue in the rod about 8cm into one side and let dry . Then you can measure and mark exactly how far you glue in the pin on the other side .Wrap repair in electrical tape .