The current control scheme is suboptimal for my play style. Can I rebind the controls to different keys, and if so, how do I do it? I checked in the pause menu, but I couldn't find anything.
Yes, you can rebind the controls. From the main menu, choose "options"
Then choose "controls"
Then choose "keyboard"
Then you will see this screen
From here, you can move between the options with the arrow keys, select by pressing Space, and choose a different key by pressing that key.
In order to change the controls mid-run, exit the game to auto-save your progress. Then follow the steps as before and from the main menu, choose "continue".