After some discussion with support and a little creativity, I use this SQL that I run weekly:
select lsrpt.Reporttitle, m.definition view_ddl , o.name view_name
from lansweeperdb.sys.objects o
join lansweeperdb.sys.sql_modules m on m.object_id = o.object_id
join lansweeperdb..tsysreports lsrpt on lsrpt.Reportquery = o.name COLLATE Latin1_General_CI_AI
where o.name like 'web50%'
and o.type = 'V';
Save the output into a table or flat file and voila - report backups!