You can do this in a more manual, but possibly easier way than @alwaysblank suggests:
- Set up a new WordPress site on the shared host,
- Drag-and-drop the plugins, mu-plugins, uploads, and themes into the new installation
- Import the database
- Find/replace in the database using this tool: FIND:
app/uploads
REPLACE:wp-content/uploads
And then test the site. With a typical, simpler site, this should do the trick.