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I have a 16 with Apple Play and just found a 4" lightning cable, plugged it into the USB in the cubby, placed the phone in the cubby and closed it up. Apple Play works pretty well to my surprise. If you have a 14 or 15, I am a big fan of ProClip mounting systems.
You can always just set the iPhone sideways in front of the shifter. If plugged into power, the screen should remain on. The problem with mounting in the cubby is you will have to keep the screen down and will not have access to the radio, etc... without always raising/lowering the screen.
My car is a 2016 2LT without factory Nav. I have an I-phone 6 with the Garmin Nav system installed. Yes, the Imap program works with Carplay, but I usually use Bluetooth instead. I also have a Pro-Clip installed to cradle the phone. Because the Pro-Clip positions my phone perfectly, I don't need a map on the factory monitor. Because of the cumbersome interaction between Carplay and Bluetooth, I find it much more convenient to leave everything on Bluetooth and skip the Carplay The I-phone screen is large enough with the Garmin App that nothing else is needed. I have full use of the monitor without the need to change out of the Carplay map to access Aps like Pandora. To me, this is the best of both worlds, and a permanent solution, even though it requires an outlay of some coin.
I get signal with my 5s just fine with it in the cubby and the vubby closed. since us want to use the pone for nav and you want cheap, I would take a 2x4 end and cut it off angled wrap velcro around it and stick a small piece of it on the back the phones case, after the trip throw it on a shelf for next time or throw it away, u ask for cheap
I think there were some in the for sale section, you might be able to save a little bit. Kenu makes a nifty holder too, its less expensive than the ProClip, but a different style of holder though.