Ok, so the missing element here is the custom php code for the widgets in the header and footer that would not be in the export. So I would have to manually redo that aspect.
Steps are then:
1. Export Css from the "Export/Import Settings" then Click on the "Export & Download Atahualpa Settings File" - save to my computer
2. Copy the Atahualpa Theme folder from the "Wp/Content/Themes/" - save to my computer
3. Copy & paste the Custom Php Code in the "Configure Header Area" and the "Footer:Content" area -- pasting the code from both sections into a notepad file.
-- Then on new host- Upload Theme folder, Import CSS and copypaste the custom code for header and footer back into the sections.
Does that sound right?