Unless something is messed up with your TP importing new books with Calibre and Kindle Import is easy. A few things to consider:
1. Calibre sends the books to /media/internal/.palmkindle
2. The . In .palmkindle means the folder is normally hidden unless viewing hidden files/folders is enabled in the file browser you are using
3. I am not sure where the eBooks folder came from but neither Kindle or Kindle Import created it
4. You need to make sure the books you are sending are in the mobi format with the .mobi extension. You can filter out all other types in Calibre to make sure you are only sending the right format.
5. You need to use the "Load New Books" button to pick up new books. You should not see books you already imported in Kindle Import unless you tap "Load Existing Books", if you have deregistered or reinstalled Kindle, or if you deleted the books using Kindle Import.
I add new books on three different TP's very often and I never have to uninstall, reregister, etc...
Add books to calibre, convert to mobi, attach tp and select usb device, make sure calibre recognizes the TP, select books, send to device, make sure the books have the checkmark next to them in calibre indicating that they are on the device, eject TP, tap load new books button in kindle import, deselect any books that I don't want to import, tap import books button, then open kindle and wait for it to refresh.