Lorenzo, I'm sorry it's taken me a bit to get back to you, but I have been thinking about your tree and doing some research.* Unfortunately I haven't come up with a definate answer.* Here's my thoughts.
1. If I cut this new branch off, I may have to train the original branch to be more vertical, as it is pretty horizontal.
True, but that might be the best way to go.* One of those sites shows how to do this with a piece of wood.
Note figure 14 here.
http://www.eap.mcgill.ca/CPTFP_7.fig14.GIF
Figure 15 here shows a similar situation that existed on the top branch on the left of the tree.
http://www.eap.mcgill.ca/CPTFP_7.fig15.GIF
2. If I cut the original branch off a short distance from the new branch, I'm not sure if this will have adverse affects on the shape of the tree.
If you allow the 'new more vertical branch' to become the leader, the space on the limb between the original leader and the 'new more vertical branch', could become a problem somewhere down the road.
Since you mention the potential shape of the tree after pruning, I have another question for you.* Are you growing the tree for fruit production or as an ornamental and whatever fruit you get is a plus?* The reason I ask is because pruning for fruit production and pruning as an ornamental are done differently.
Newt
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.