There was this one gameboy game I played a long time ago so I don't remember the name. But I do remember it was a shooter and the way they made strafing work was if you only pressed the directions, you would turn like in this game. When you held down R, it would freeze the direction you're facing and you'd go into strafing mode essentially.
I don't know whether that's the best idea or if it would work for this game, but it's just an idea to think about right