A standalone strafe button. I've thought of that, too - the Game Boy port of Contra 3 has B to shoot and holding A to strafe on the top-down levels - but I haven't tested that yet either 🤔 Plus even in that setup, the player would still be required to face the direction they want to shoot before holding the fire button.
It's certainly a control setup I'll want to try to recreate at some point though; I've got plans for many demakes, and that control scheme is bound to be an ideal fit for something.