Don't know about the Ibanez but I have a custom headless with ABM hardware and there are many strings that refuse to be clamped.
So, strings I've tried to use with my fretless but have resulted in destruction; TI flats, La Bella nylons, Galli Synthesis, DR Sunbeams.
Not saying the Ibanez will do the same but non double ball end strings in general are not designed to be abused in this cut & clamped way.
I think by going headless you are restricting the type and number of strings you can use.