I went to North Cyprus for a recent and most enjoyable holiday.
It's true all flights have to land in Turkey first. Ours from Manchester went via Dalaman, so not so far out of the way as Istanbul. Stay on the KTHY B737-400 for 30 mins of refuel and partial crew change so no problem other than the fact that it adds about 1.75hrs to a direct journey if it were possible. Bags and tickets were to ERC but flight was (always) to the other one due ERC still being closed.
Although it is a military airfield there is no hassle. Bags were quick and, in fact, we were waiting outside for the arranged pick up, bags at our side, some minutes before the due arrival time!
Return from same airfield. OK it's a little place with only two non descript duty free shops, but all the better for it IMHO.
Nice place, the TRNC.