Well, I suppose you first need to consider what's doing the work on a guillotine; as far as I can tell it's only using gravity to drop the blade. So we'd want to reduce any friction caused by the rails, it'd be easiest to upgrade to aluminum and get some sort of ball bearings or something to keep it as low as possible. Obviously we want a sharp a blade as possible - considering our lack of sustained killings it might be best to move to a one use blade mechanism to keep it pointy since we probably don't have to worry about durability with sustained beheadings.
Hmm, after that we should probably try to introduce more energy into the system since we're still just using gravity. Adding more weight would probably help but wouldn't ever make it go faster than terminal velocity. Maybe the cheapest option would be spring-loading the top of the guillotine so after the lever is pulled it shoots down. Or if you want more future-y could try to make some sort of magnet railgun to propel the blade down at increasingly fast speeds.
For the bottom it seems pretty good, though you'll want to make sure you have the executioner line up the blade to be in-between the vertebrae (gotta try and make it as swift as possible). Then maybe add a pillow, because it doesn't look super comfy there.