When we use the epitope_id's we have in our database to try and make links instead, many of them give us blank pages

I believe you are attempting to use the old IEDB IDs within the new link format and this is producing unexpected results.  For example, the epitope with sequence SWYEKYNIV that you referenced has an IEDB ID of 1117733 in the legacy site.  If you try to connect to http://www.iedb.org/epId/1117733 you will get an empty epitope details page (we have a ticket to improve the error reporting for users that is slated for completion in the next build).  However, if you use the old httpQuery format http://www.iedb.org/httpQuery.do?dispatch=runquery&eid=1117733, you will be properly redirected to http://www.iedb.org/epId/62506, which is the epitope details page for the logical epitope that SWYEKYNIV is associated with.  This may help provide a short term fix that will reduce the impact of the change while the sites are updated to provide for better integration.