Okay, something is not adding up. As GLR implied, everything upstream of the sending unit is fine. We know this because a test light blinks at the sending unit lead, and the gauge pegs toward FULL if you ground out the lead. All good there.

But if the sending unit reads less than 10 ohms (even zero), the gauge should be pegging FULL with the sending unit connected. But you're saying that's not what happens.

You're giving many pieces of information that by themselves are very helpful, but contradict one another when put together. One of the things you're saying is true is in fact not true. I'd start by double checking your sending unit resistance measurement. Let me know if you need help using your multimeter. If you think you're checking it correctly, then please at least describe how you're capturing the measurement.