Where are the Original files? You're going to need them?
Are you running a Managed or a Referenced Library?
A Managed Library, is the default setting, and iPhoto copies files into the iPhoto Library when Importing. The files are then stored in the Library package
A Referenced Library is when iPhoto is NOT copying the files into the iPhoto Library when importing because you made a change at iPhoto -> Preferences -> Advanced. The files are then stored where ever you put them and not in the Library package. In this scenario you are responsible for the File Management.
But then I get alert after alert about not being able to open photos because the originals can't be found.
That message turns up when you have a Referenced Library but this
When I used Spotlight to look up the filename and then 'reveal in finder' it was jumping to 'Masters'.
is a Managed Library, so I can only guess that iPhoto is more than somewhat confused.
Back Up and try rebuild the library: hold down the command and option (or alt) keys while launching iPhoto. Use the resulting dialogue to rebuild. Choose to Rebuild iPhoto Library Database from automatic backup.
If that fails:
Download iPhoto Library Manager and use its rebuild function. This will create a new library based on data in the albumdata.xml file. Not everything will be brought over - no slideshows, books or calendars, for instance - but it should get all your albums and keywords back.
Because this process creates an entirely new library and leaves your old one untouched, it is non-destructive, and if you're not happy with the results you can simply return to your old one. .