I think I may have resolved this.
When I created the Upgrade project from our original project, I evidently didn't update all that I should have such as the namespace, dll name, etc.in the project settings. These still had the original project name. I also tried to "get by" without being able to load the Upgrade app in iis - I had assumed it was some other configuration problem outside of visual studio. Bad move.
After getting the Upgrade project to build and load in iis, I ran the conversion. I had to drop and re-add a reference to another project on my first build attempt. As soon as I did that I got 383 errors and 53 warnings but the info in the error messages is enough for me to work with. For a lot of the errors, they are duplicates, so once I fix it, the number should drop quickly. I'm no longer seeing the "Could not load type..." error message, thank goodness.
Once we get the current build to compile successfully and run, I think we'll use the Convert to Web Application context menu that you mentioned above to convert to using partial classes. Previously, I wasn't sure where that menu came into play.
Thanks again and sorry for the trouble.
Don