Shout out to you guys for all your help and suggestions! I ended up going with Ross's idea. This is the sending unit I got:
I drilled a 1.5 inch hole for the sending unit to slip down in, and then 5 holes for it to bolt up to. Be weary of the "slosh/support rail" in the bottom of the tank when deciding where to put it. I bought new hardware as well. This is how it turned out:
The wiring was easy. On the fuel pump connector, you SPLICE one end into the black ground wire and CUT the purple wire and connect the second end to that.
The only downside is the sending unit is pretty cheap, so it doesn't use a continuous resistor. That means your gas gauge is only going to read in ~6 positions. My gauge didn't work at all so this is a huge improvement for me. I've run out of gas twice. Hopefully this will remedy that habit.
I might provide an update as to how much fuel the car takes when my gauge shows empty. I'm hoping around 6.5-7 gallons. They are 9 gallon tanks right?
Thanks again for everyone's help!