I've walked in that area several times and the Lycian Way is very well marked. However, once you get off of the marked pathway there are some treacherous drops and hundreds of places into which a person/body could disappear.
I'm pretty sure that AKUT and the Jandarma have far better resources and local knowledge of the area than any of us. They'll have villagers from Kirme and Faralya, and local walking guides, who have intimate knowledge of the terrain working with them in a methodical search. They're also using microlights and a helicopter to assist in the search.
I don't think we'd be doing them any favours by turning-up and doing our own thing and I doubt that they'd be willing to share information about un-searched outlying areas with "outsiders" at this stage.