I don't know what you mean by "snap your wrist even more" but don't do it. In tennis, any wrist movement (snap, bend, pronation, etc) is a natural result of the swing and not a conscious movement done by the player. If you want more spin on your backhand, play with a looser wrist (relax your left arm which is the dominant arm on a right-handed player's backhand). Also you'll need to brush up on the ball so you'll need to change your swing path, starting a little lower and finishing a little higher - the right knee-bend will help, as will not lunging on that final step to short balls.I'll post a video of an actual game when I'll have one. I'm also curious watching myself play.
I can hit heavy spin and fast balls with my forehand, but not with my backhand. I kind of lack power. Probably should bend my knees and move more. People say I'm pretty static. Is my swing too short, should I snap my wrist even more?