Experienced travelers to Crete tend to use locally owned car rental companies. Since they are not part of big chains they get their business through good service and word of mouth.
I have experience with Athenscars Crete and Autorentals. Other companies with good reputations are Anna cars and Best cars. Go to Trip Adviser and search for reliable car rental companies Crete. You will see that these companies have a lot of support.
This year we are renting again from Autorentals. We are arriving Chania by bus and they are picking us up at the bus station and taking us to the airport where their rental depot is located. Last year we had 24 hours of travel before we arrived in Heraklion. I didn't want to drive jet lagged so they delivered the car to our hotel in Sissi a village half an hour from Heraklion. Local companies work hard for your business.
Insurance
These companies all include full insurance with no deductible as part of the price. Just a couple of things to remember though. The insurance is nullified if you are driving on a gravel road. Any damage to underside of the car or the tires will be charged to you.
Secondly the insurance covers the vehicles and does not include third party liability. We have a special rider on our home insurance that covers us for personal liability. Your gold credit card does not provide this coverage.
Lastly the insurance covers the vehicles, yours and the other persons vehicle. Your insurance comes into play if you are at fault. If the other guy is at fault then his insurance has to pay. I have heard of Greek drivers telling tourists"well you are insured" and just driving off. Thats when they discover if they you are not at fault the insurance that is included doesn't cover.
Our rental guy told us to get pictures of the accident scene, the other guys license plate damage to both cars and if possible the other guys license. This is all good stuff to know.
The other thing that is outside the norm is these companies operate on a very casual basis. They don't have offices at the airport but rather in a compound nearby.. They meet you at the airport and transfer you to their compound where the paperwork is done. This is what I described earlier with pickup at Chania bus station. Last year I did my paperwork with Autorentals at their depot at the airport then took a taxi to the hotel where the car was waiting.
Drop off can be very casual as well. Several times we have rented in Chania and dropped the car off at the Heraklion port. They just tell you to park in a certain area, pay for an hour parking, lock the key in the car and head off. They will collect the car later. It sounds odd but it works well for these companies. On several occasions we have had early morning flights and arrive before the staff arrive. We just dropped off the car and the security guard drove us the kilometer to the airport. No fuss no bother.
Oh yes glad to hear your have your IDP. You do know though that you still need your own license. I have heard stories about people leaving their license at home because they have the IDP. Bad thinking.