I decided to detach the page from its layout and add the DataView Web Part. Everything seemed to work, except I started to receive errors stating "This Web Part Page has been modified since you opened it." I figured this was related to detaching from the Page Layout (I may have hosed something up unknowingly). I then reattached the page to its layout and everything ended up working fine.
Therefore, if you need to add a DataView Web Part to a page attached to a layout, I suggest doing the following(all done within SharePoint Designer):
- Detach the Page from the Page Layout
- Go through the necessary steps to add a DataView Web Part to an existing zone on the page
- Reattach the Page to it's Page Layout
Note: I have not attempted to reattach a page to a layout after new zones have been added and do not know exactly what will happen.