Since Carbonite turned out to have those two severe limitations, I went looking for other online services. I really liked the unlimited backup size and the online accessibility of Carbonite. But after using DropBox, I don't really need to have my backups to be accessible from my devices. Most of the time, I'm going to need them from my laptop. Luckily, I found an online provider that has all of these features: LiveDrive. We'll see how well it holds up as I give it a spin for the next couple of weeks.
Update: After syncing 12 hours, it has uploaded 4GB or so.
Further update: after 36 hours, we're up to 12GB or so.