An update: In fooling around with the wires connected to the antenna jack on the back of the radio, I noticed that when I disconnected the cable going up in the wall (which I assume goes to my omnidirectional TV antenna), my fm reception improved dramatically with just the small piece of coax that comes off the antenna jack. It appears that not only does the omni not do any good for reception, it actually hurts it.
For this reason, I ordered an $11 replacement antenna from Amazon that comes with an F connector. I plan to connect that antenna to the outside "cable/satellite" connector and then see if my reception improves more.