I was able to extract my user list from my old host mailman list with the following command:
sudo /usr/sbin/list_members -o [my_subscribers_list.txt] [my_list_name]
Once I had my list of subscribers, I was able to "mass subscribe" them all using the mailman administrative interface at 'lists.[mydomain.com]'.
As for the archives, a support person named Robert contacted me, and said:
"Is your mailing list an archive and do you have it in .mbox format? If so, just upload it to your webspace, let me know it's location and I'll import it for you."
So, I tarred up my mailman list archives and placed them in my dreamhost web space.
So there we have it. The support folks can migrate the archives.