Last went to Rhodes 3 years ago. At the time was looking for scheduled flights but none available. Went with Falcon but Sunway, Panorama and Stein Travel (??) also went.
Found out nearer travel time that I could have gone by scheduled flight to Prague and direct to Rhodes from there with the same airline Czeck Airways (??), through baggage etc and 90 min stopover.
Don't know what the current situation is but may be worth your while to suss out the Prague link. Very few other direct scheduled flights available from anywhere to Greek islands - vast majority seem to go through Athens.