Ubuntu – Ubuntu 14.04 to 16.04 upgrade broke the ZFS

I just upgraded Ubuntu from 14.04 to 16.04 which seems to have broken ZFS. I followed the directions here and purged all old ZFS packages. I then installed zfsutils-linux from the default 16.04 PPAs but whenever I run any ZFS commands I get the following error:

:~$ sudo zfs get all
The ZFS modules are not loaded.
Try running '/sbin/modprobe zfs' as root to load them.

I've attempted using modprobe as the error messages recommends:

:~$ sudo /sbin/modprobe zfs
modprobe: ERROR: could not insert 'zfs': Invalid argument

It seems like ZFS is not installed but apt-get shows that it is:

:~$ sudo apt-get install zfsutils-linux
Reading package lists... Done
Building dependency tree
Reading state information... Done
zfsutils-linux is already the newest version (0.6.5.6-0ubuntu16).
0 upgraded, 0 newly installed, 0 to remove and 3 not upgraded.
N: Ignoring file '50unattended-upgrades.ucf-dist' in directory '/etc/apt/apt.conf.d/' as it has an invalid filename extension

I also physically went to my machine rather than using SSH to watch the boot and saw a number of ZFS items FAIL on startup, one of which I believe said something about dependencies, but it went by too fast for me to read all of them. I attempted to see what they say by looking in boot logs, but I've been unable to find a boot log file that matches the output shown during startup. Where can I look to see what is actually failing at startup?

Further interesting discovery is that if I use just the zfs command, I get the 'missing command' output, but when adding any command I get the same error message from above.

:~$ zfs
missing command
usage: zfs command args ...
where 'command' is one of the following:

        create [-p] [-o property=value] ... <filesystem>
        create [-ps] [-b blocksize] [-o property=value] ... -V <size> <volume>
        destroy [-fnpRrv] <filesystem|volume>
        destroy [-dnpRrv] <filesystem|volume>@<snap>[%<snap>][,...]
        destroy <filesystem|volume>#<bookmark>

        snapshot|snap [-r] [-o property=value] ... <filesystem|volume>@<snap> ..                                                                                                                                                             .
        rollback [-rRf] <snapshot>
        clone [-p] [-o property=value] ... <snapshot> <filesystem|volume>
        promote <clone-filesystem>
        rename [-f] <filesystem|volume|snapshot> <filesystem|volume|snapshot>
        rename [-f] -p <filesystem|volume> <filesystem|volume>
        rename -r <snapshot> <snapshot>
        bookmark <snapshot> <bookmark>

        list [-Hp] [-r|-d max] [-o property[,...]] [-s property]...
            [-S property]... [-t type[,...]] [filesystem|volume|snapshot] ...

        set <property=value> <filesystem|volume|snapshot> ...
        get [-rHp] [-d max] [-o "all" | field[,...]]
            [-t type[,...]] [-s source[,...]]
            <"all" | property[,...]> [filesystem|volume|snapshot] ...
        inherit [-rS] <property> <filesystem|volume|snapshot> ...
        upgrade [-v]
        upgrade [-r] [-V version] <-a | filesystem ...>
        userspace [-Hinp] [-o field[,...]] [-s field] ...
            [-S field] ... [-t type[,...]] <filesystem|snapshot>
        groupspace [-Hinp] [-o field[,...]] [-s field] ...
            [-S field] ... [-t type[,...]] <filesystem|snapshot>

        mount
        mount [-vO] [-o opts] <-a | filesystem>
        unmount [-f] <-a | filesystem|mountpoint>
        share <-a | filesystem>
        unshare <-a | filesystem|mountpoint>

        send [-DnPpRvLe] [-[iI] snapshot] <snapshot>
        send [-Le] [-i snapshot|bookmark] <filesystem|volume|snapshot>
        receive [-vnFu] <filesystem|volume|snapshot>
        receive [-vnFu] [-d | -e] <filesystem>

        allow <filesystem|volume>
        allow [-ldug] <"everyone"|user|group>[,...] <perm|@setname>[,...]
            <filesystem|volume>
        allow [-ld] -e <perm|@setname>[,...] <filesystem|volume>
        allow -c <perm|@setname>[,...] <filesystem|volume>
        allow -s @setname <perm|@setname>[,...] <filesystem|volume>

        unallow [-rldug] <"everyone"|user|group>[,...]
            [<perm|@setname>[,...]] <filesystem|volume>
        unallow [-rld] -e [<perm|@setname>[,...]] <filesystem|volume>
        unallow [-r] -c [<perm|@setname>[,...]] <filesystem|volume>
        unallow [-r] -s @setname [<perm|@setname>[,...]] <filesystem|volume>

        hold [-r] <tag> <snapshot> ...
        holds [-r] <snapshot> ...
        release [-r] <tag> <snapshot> ...
        diff [-FHt] <snapshot> [snapshot|filesystem]

Each dataset is of the form: pool/[dataset/]*dataset[@name]

For the property list, run: zfs set|get

For the delegated permission list, run: zfs allow|unallow

What else can I do to troubleshoot this ZFS install?