"If I take the lead that goes to the sender and take it off the sender, the gauge shoots way past "F"."
If your needle goes to full when you disconnect the sender, that usually indicates that the gauge is good.
"If I than ground the wire, the gauge weakly attempts to move the needle back, but will either not move it, or move it back only a tiny amount."
What wire are you grounding? The wire from the gauge to the sender (dsconnecting the wire at the sender and grounding that end of the wire)?
Someone else might have advice about grounding the gauge itself.
It looks to me that you might have a bad sender, or, a bad tank-to-ground connection. I have seen people place a ground wire from a sender-to-tank bolt to clean metal on the frame/cab/etc.
