I'd like to have some way to back up an individual sub-account (or group of individual sub-accounts) from within Webmin. Ideally, I should be able to specify what to backup, i.e., the entire sub-account, email for the sub-account, or specified directories within the sub-account. The backup should be capable of automatically assuming whatever privileges are necessary to create a gzipped/bzipped tarball of the targets, and then email a link to the tarball for easy downloading to a remote server.

I guess you're talking about Sub-servers...which can already be backed up with pretty much all of the features you're asking for (and more). I believe the download backup link feature just came in 3.50 or 3.51, but it's all there.