You could always enable email move notifications and keep checking for new mail - that would shift the load to your mail server.
All pages on the RHP site have the red bar at the top with the 'N games waiting' text - if you picked one of these that contains mostly static information (or at least information that doesn't depend on who is looking at it) then refreshing that might not put too much of a load on the server, but it will eat up bandwitdh.
I think either the list of forums or the list of open invites might be among the cheapest pages to refresh, but mail notifications must be best.