The best thing I was able to come up with as a quick workaround was to upload the artifacts in question to my FTP server via curl, as suggested by my original question. It works, but the downside are the FTP credentials in the build public log. I have counterbalanced that by a shell script on my DSL router which checks for FTP storage abuse every few minutes.
As an alternative I found that after creating a free CloudBees account for my little open source project, I got my own Jenkins build configuration as well as my own artifact repository where to deploy my build artifacts. This is much more elegant and does not involve posting any FTP credentials to a public server.
I am still open for BuildHive-only solutions if anyone has a smart idea. :-)