I resolved the core.img is unusually large problem by expanding the boot partition.
I was reinstalling a server yesterday and I found that Fedora 16 Anaconda will put a 1MB partition first in order to boot, before adding the 500MB (current standard) partition for /boot.
On the first machine, one of the tasks I completed in order to assist in troubleshooting was to create a USB key with Grub2 on it to boot the machine into Fedora. That left me with Windows dual booting just fine and allowed me breathing space to troubleshoot and use gparted to solve my problem.
Put these Grub2 Linux bash commands into Diigo today so you have them when you need them. A reminder that GNU GRUB is a work in progress and the information in this website is incomplete and may be wrong and/or out of date. Please consult the official GNU GRUB 1.98-r2692 manual as well. Still I did use the commands for Grub on a USB and they worked after I translated configuration file locations from grub to grub2.