Thanks for the replies. The database is about 550 Gb. We made a couple of strategic errors with the server, so we're looking to move this database off to another, better equipped server. Until we had contention problems we were doing weekly full, nightly diffs, and half hour t-log backups, but we had to make compromises due to contention on the server.
We're going to give the full backup plus t-logs a try. Hopefully that will get us fully restored, and if that doesn't work, we'll have to try the full-diff-recent t-log route.