I've removed Web Forms and a Picture Gallery from my Website Design in VSD. I notice in my saved files that the site still carries files related to the old Flash Elements. When I upload my site, I get warnings that files are missing, in reference to the old Flash Elements. Once loaded, my new Web Forms, labeled with a completely different name, do not function.

When removing any objects "flash or files" you should also use the remove files to remove the old files from VSD, as you know you'll get those errors.
do a save after removing and then add the new form files using the flash tool
you should be ok using this method.