You could measure the background noise in the car with an app on your phone.
D50 is powered by a USB line so a power bank or just a car charger will be fine. 2RCA to 3.5mm aux into your head amp and you’re away. Hope you have some mother quiet amps and some great speakers though.
9038s won’t work, as it’s balanced out. Your Fiio (or a UP2) should be quite good as you can just leave it dangling from the aux in. I still use an iPod in the car, as they might give me a ticket if I’m seen changing to the next track on my phone.
If you do end up doing it, let us know how it goes. I wish I had a nice quiet car.