I'm looking for a command line tool that can install a package from a file and automatically resolve dependencies via download. Does such a thing exist?
You are probably looking for the tool gdebi
gdebi lets you install local deb packages resolving and installing its dependencies. apt does the same, but only for remote (http, ftp) located packages.
After playing with it a bunch I see what's going on now. You dpkg -i whatever.deb and it will load it on the machine in some broken capacity but not completely install it, then you run apt-get -f install and it will download and fix up the dependencies for you and then it will complete the install process of the deb package. Not pretty but it works, and I'm happy.