Ok, I was able to fix it in what appears to be a non-destructive way. Here's what I had to do:
vzctl exec 104 rpm -e --nodeps kernel udev mkinitrd module-init-tools
Then I copied the dummy and vzdev packages where I could get to them inside the vps
vzctl exec 104 rpm -i /var/cache/yum/base/packages/dummy-fedora-core-4-1.0-3.swsoft.i386.rpm /var/cache/yum/base/packages/vzdev-3.3.13-1.3.swsoft.i386.rpm
Then I restarted the VPS and I was able to successfully enter it again. The package removal hasn't seemed to hurt anything but time will tell. Now to avoid the situation in the future...