How can I set up Arcade-like physics with ACharacter?

Because you want no acceleration, and an arcade spaceship moves so differently from a biped (which is what Character is designed for), I would recommend extending from Actor instead of Pawn or Character.

Here’s what I would do. Make your Spaceship class extend from Actor. Then, have your Controller class spawn your Spaceship class in BeginPlay(). Save a reference to it in your Controller class when you spawn it. From there, you can manually specify any movement by using SetActorLocation() through your input events in the Controller. No unwanted built-in physics, no excessive unnecessary code that comes along with Pawn and Character, only what you need.