A consideration of an upward-striking hammer is that you have to have some method of preventing damage to the mechanism as the hammer reaches the surface being struck. This could be the absorption of energy or the displacement of the item/surface being struck. Recoil is the method used in the gravity-fed DaVinci design.
A couple of methods come to mind, but I'll focus on one. Consider DaVinci's design, but place the cam under the lever end containing the hammer. As the cam rotates, the hammer falls to a conveniently placed platform.
The other end of the lever is extended and also has a hammer head attached. As the cam rotates and the first hammer falls, the second hammer rises. It should be configured to strike the desired surface before the first hammer contacts the platform, for optimum results.
In the above described configuration, the weight on the first hammer end has to be greater than that on the second hammer end. The placement and size of the cam allows for flexibility. One could place the cam outboard of the first hammer head and have a substantial size and displacement, for example.
You've noted that the mechanisms you've found appear to stop the hammer at the upper surface. This is to be expected if you are striking this surface. Will you expect your upward-striking hammer to move the surface it strikes?
If so, your design will have to allow for greater travel via cam diameter, displacement and location along the lever.
If this does not appropriately address your design considerations, please provide additional constraining criteria.