I would imagine that you could. It would probably have to be done with some kind of expression. I had to make a bunch of crazy one's for my game and I am no programmer, so don't get overwhelmed with expressions. C2 makes them pretty easy to do. I would guess it would be something like this:
when you press left arrow = player.X(+32)
right arrow = player.X(-32)
up arrow = player.Y(-32)
down arrow = player.Y(+32)
player would be the name of the sprite you want to move. That sprite would probably need a behavior so it would go threw other solids. Solid might work or a 8way movement with the default controls set to NO.
Also you mentioned getting stuck. You won't get stuck on walls(solid) if they are position exactly next to each other with the collision set to bounding box on them. In other would don't leave little jaggy edges on your walls.
Also Thank you for the review it was well written! I'm sure you bought the game because you can only write a review after you buy it, but for some reason I can't find your info on the merchant end of google. I think that the chrome store may be on a bit of a delay or just plain buggy. Would you mind telling me the name of the email it was purchased under? This is just me debuggy google.