hmmm ... not sure how many images they're hosting... but here's a thought ... instead of just killing the images, why not reduce just server some very low quality images instead, in order to reduce bandwidth and storage costs (allowing you to reduce the number of servers)
ex save anything to 20-30% jpg quality ... anything bigger than 640x480... maybe resize by half.
for example the image below is <30KB saved as 20% quality jpeg, from a 500 KB sample image

maybe add a tiny black bar at the bottom of picture saying Image served at reduced quality. visit tinypic/full/==code== to download at original quality ...
Keep the original pictures in the user's account and let user export them to quickly by making a zip or someting...
maybe they'd be willing to sanitize their database (remove personal information) and make it available, so anyone could parse their forums for tinypic links and grab the images and upload the images locally and then do a mass replace.
Nowadays there's 1gbps unmetered servers for less than 200$ a month... so not sure how much traffic tinypic does to not be able to keep it alive.