Thanks for the offer!
We tend to keep the pictures on Photobucket, exactly because of bandwidth and storage/backup reasons. The site backup was getting pretty large until we moved all the images out. It still is big as the phpBB database is old and clunky with some stupid index tables that take up almost as much space as the posts!
We're looking at moving hosting to something with a bit more storage and power to cater for some potential side projects, but mainly for performance and because there have been some periods of unavailability that were either unplanned or I was never told about. In themeantime, let's see if the small tweaks I made have banished those timeouts.
Oh, and if anyone has a recommendation for a hosting service that does not oversell capacity, please drop me a PM and I can add them to the list.