Is the drum of your unit the turnbuckle body?
Can you undo the turnbuckle, thus raking the mast
Or, maybe if you unscrew the top thread an inch (that's the stud) and screw in the bottom thread (that's the toggle) you will have a longer wire without changing overall stay length. I think the threads are different so you may do 18 turns for the stud, if you have a 5/8" thread, but only 16 on the toggle.
Not sure if that will work but I am sure I will be corrected if there is someone out there with a Harken furler
. Be carefull to leave enough threads of the stud screwed in. Good luck