I've never needed to set one up in a DOSbox-run game before, but it seems like it might enhance the experience here. Anyone know how to do it?

Sorry for the late response, but better late than never. ;o)

I have to recall this from my memory because it is over a year ago that I played this.
This game supports a joystick, you should be able to choose it from within the game menus.
Though I think the game didn't support a throttle and rudder, you could only control your speed with a button/key.

I'm not sure how the GOG version is configured, but there is a .conf file in the gamedir that you can edit using notepad. I always had timed=false for the joystick as it is less jerky then but perhaps it also depends on the type of joystick.

It's been a while I know, anyway, the game has an option to choose if you are going to choose keyboard, joystick etc for control. After you choose joystick you just choose what to use for Fire, Select (weapon or turbo), Accelerate (there is no brake).

The game also has an in built "calibrate joystick" option, though I am not sure since it is running through emulation if that matters at all or not.