odin doesn't recognize my phone
Anyway, I did install the modded CWR you provided ("CwM Voodoo Lagfix Recovery v2.5.1.x", apparently) by copying it onto the SD card in those two places, and when booted it is able to access the SD card. Yay! I can now tell ROM Manager to make a backup and it reboots into the new recovery and makes a backup.
Changing the kernel didn't seem to affect anything - the original CWR still fails to access the SD card if I install it through ROM Manager. As far as I can tell, the modified CWR is what fixed this problem.