Not certain this would work as haven't tried but...
If you're using SQL to store your BEWS info rather than MSDE, you could try going into Enterprise Manager, and creating a flat file backup of the Backup Exec database within it's SQL instance, this all the data relating to your jobs, selection lists, media sets etc are stored in here. Then when you re-install BEWS, shut down the services (except the SQL instance service) to be on the safe side, do a flat file backup of the newly created SQL database (just in case this doesn't work), and then using EM restore your backed up copy of the SQL database over the new one. Hopefully then when you re-start BEWS you'll find all your settings have been restored to their rightful places.
As I say there is a definite element of guesswork to this, but if you can't find a more definitive way of doing it this might be worth a try. Worst case scenario you have to re-install BEWS again, and end up exactly where you would have been if you hadn't tried.
Keith