I found my answer; it took a while, so I'm posting it should anyone else be searching for something similar.
It was really a pine configuration thing. In pine you can create Collections of mail folders or just enable Incoming folders. At my old host, I'm the admin, and I can quickly use my shell login to run through various mailboxes and spam traps on various domains, save various messages into ham and spam folders, and run sa-learn for spamassassin.
But that won't work at DH. They have it set up so that the owner of a site can't view mailbox contents or junk contents for various domains and users from the main shell. Unless the owner logs into each user's shell individually and runs spamassassin that way. Or, you can just enable filtering in the panel, and not get into all the nitty gritty.
I kind of have to. Fortunately, I only have a couple users to set up, so I can probably make it work.