Well, looks like you're in the right place to find something
So, without knowing the dates you are arriving, I just did a quick search for eight days (ICR seems to do this by default anyway - and it means if you have a late flight home, unlike your package hol companies, you aren't kicked out at 10.00am and have to hang around all day, you can have a snooze, take a shower - have the apartment right up until you leave) from 3rd September, and there's plenty of accomodation in Icmeler. The Rhodes apartments are available, and these are highly rated on here - just one example - comes to £200.
Now you already have your flights with your package deal - might as well keep them, they're bound to be good. The
transfer though will be to
Marmaris by coach. You don't want that, and it would be a faff and a half to get a taxi from Marmaris to Icmeler, not to mention a mad way of doing it.
Simply when you book your accommodation on ICR, book a transfer too. It's superior (In my opinion) to the slowcoach the package companies do

. Cost is £90, so in total that would be £290 extra for you all. Course there can be cheaper or more expensive accommodation - but that's your choice
If that sounds good, why not go for it...now
Oh, and if you do, don't forget to find the package company rep at the airport, just to say you aren't taking them up on their transfer. It's just polite, and it is really inconvenient to everyone else when someone otherwise doesn't tell them, and they're frantically looking for them all over the arrivals lounge.
Hope this helped.