I don’t know how big and how accurate your saz is regarding note intervals, but you don’t have to worry much. Here in Greece, the vast majority of Rebetiko fans plays the bouzouki, accompanied by guitar and the small “Greek” baglamas as typical orchestra. All these instruments are fretted, so no movable perdeler come up. When tunes are played, that were originally recorded obeying the “classical” intervals like e.g. Aeroplano tha paro, we simply disregard the individual interval differences.
Although Greek “Dromoi” actually derive from the respective oriental makamlar, the western tones / semitones are used. It is advisable to follow a modal approach rather, than a scale oriented one. I don’t know of Apostolidis’ book but I would strongly advise the “Laiki kithara” (folk guitar) book of Dimitris Mystakidis. You can either buy the book or download it for free, e.g. from this link: https://www.openbook.gr/i-laiki-kithara/
And something more: You probably have not heard of (the late) Marios Mavroidis. He has written a very good book, today a classical standard, presenting and comparing the modal approach of music in the Eastern Mediterranean, i.e. the byzantine Echos, the arabian makam and the Turkish makam. Somewhere in the introduction, where he observes different definitions of intervals in those three approaches, he makes the following note, to which I fully agree: Regardless of the “official definition”, which is no more than perhaps one or two centuries old anyway, all traditional interpreters would always prefer to stick to their personal approach rather, than strictly complying to what Rauf Yehta Bey or Simon Karas of Greece or whoever theorist has thought of, often following national or other non – musical rules in the early 20th century. So, feel free to develop you own style with your saz!
Well, it’s somewhat difficult to try to communicate via keyboard… My main point is that at least in the beginning (from 1932 on), although played by well tempered instruments, rebetiko kept its modal characteristics.