If you think that sender might be destined for the garbage can, then it probably wouldn't hurt to try a few rescue efforts on it before you get a new one.
If you think it might just be that it's not sliding smooth anymore, it could be there is some gunk in and around the inside of the column or the float. I wonder if maybe you tried to soak it overnight in some kind of degreaser if that would help free it up? Not sure what you might use though. Heck, try dish soap perhaps, but just get it all off before you dip it back in the fuel tank.
Or are you saying the float doesn't float anymore? I have never taken one apart, but I wonder if that float could actually break open a bit and basically get filled with fuel. "Water logged" sort of. I guess if you run out of options you could try and dismantle it and see if you can figure out what the problem is. Again, I don't remember what goes on inside the sender really or how you would take it apart.
Last time I checked, DMCX sold fuel senders for $99. And if I'm not mistaken they might be better calibrated than the old originals. Like another member said, you could conceivably go with the fuel pump & sender combo, but if your fuel pump is fine, that's a bit of an overkill.
The good news is it sounds like everything else from the sender wiring back to the gauge is working fine.
As for you wondering if there was something else making you stall other than just running out of gas, I would suggest solving the thing you know was a problem, that being that you added some gas and it started right up. I would chalk the engine dying up to no fuel until proven otherwise. You could start doing all kinds of things not even knowing if they were really a problem in the first place. You're right though, get the fuel gauge working and figure out how much fuel is in the tank, then subtract that from what you added. If it wasn't an empty tank causing the problem, we'll tackle that next
