Meant to report this earlier. Ahem. Basically, closing the Steam Overlay (once allowed via the -opengl launch parameter) can cause the keyboard controls to become semi-unresponsive. You don't have to have done anything to cause it to freeze. Sometimes it works, sometimes it doesn't. Sometimes I have to open and close it another time to get the WASD keys working again (I believe 'Esc' continues to work as normal). No idea exactly what's causing it as it's seemingly random.
This is known because the overlay works very weirdly with DoD, as you said only works with a workaround. I wouldn't expect to see it fixed at this point but who knows. Maybe Nicholas can shed some light on this if he gets the time.
Oh, of course! It could just be due to DoD and the Steam overlay not being best buddies and nothing else.