Update: I purchased the fuel signal adapter module from Autometer and installed that today.
https://www.amazon.com/gp/product/B085D76YX6/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1
By using the "Learning" mode on the module I have been able to get the gauge to read much more accurately. With about 10.5 gal in the tank it is now reading slightly above 1/4 tank. That's still not exactly right (should be closer to about 7/16 tank) but it's way better than "E" which is what the gauge was reading with the same amount of fuel but without the module. As I drive it and see how it reacts to different fuel levels in the tank I should be able to tweak it a little more but this is good enough for a starting point.
I also made my life way easier by cutting an access opening in the floor so I can get to the sending unit without dropping the tank. You can see what that looks like in the photo I added in one of my previous posts in this same thread.
That made making adjustments on the module so much easier because you absolutely need to have access to the sending unit in order to make those adjustments. You could still do that without the access opening but you have to do it with the sending unit out of tank which means without the opening you would have to do all that before you install the tank. If I need to make any future adjustments to the gauge all I need to do is remove six screws and pop the "door" off.
Here's my crazy theory on why this new sending unit is so inaccurate at the lower fuel levels:
The gauge is nothing more than an Ohm meter. In other words, it measures resistance to electrical current. As the fuel level drops so does the float. Since the sending unit shaft is a solid metal (stainless steel) rod there is more resistance in that rod the closer the float gets to the bottom of the rod because the electrical current is effectively having to pass through more of the rod.
The higher the amount of resistance (Ohms), the lower the gauge reads. It's not supposed to read "E" until it sees 73 Ohms but in my case the gauge was reading "E" at 53.1 Ohms or 6" from the bottom.
My theory is that if the rod were tapered so that it was a smaller diameter at the bottom than it is at the top, there would be less resistance in the rod than there is now as the float gets closer to the bottom which would allow the gauge to read higher than it did without the module. I have no idea how to calculate the amount of taper required but knowing that it requires a measured 24 Ohms for the gauge to read accurately with the amount of fuel currently in the tank (10.5 gal) should be a starting point.
There obviously also has to be enough resistance in the shaft when the float is at the bottom of the shaft so that the gauge will still read "E" when the tank is empty and that would limit how small the diameter of the rod can be at the bottom.
Another, and perhaps easier, way to do the same thing might be to drill a hole in the bottom of the shaft or even a series of small holes through the shaft. However you do it the goal would be to remove just enough mass but not too much.
The bottom line is it needs to read "E" when the tank is closer to empty, not when it is nearly half full. And if the sending unit were more accurate you could eliminate the need for a signal adapter module.