Try a different slosh module and cluster gauge. Supposedly they are not "matched", but in my experience, when you mix slosh modules and gauges you get inaccurate readings. So take a trip to the boneyard and get a cluster from the same "era" Mustang (87-89, 90-93). Put both the module and gauge in your cluster and see if you get an accurate reading.
I hate just throwing parts at cars, but sometimes it is the easiest way to find a problem.
Did you use the multi-meter on your new in-tank sender, to make sure it reads correctly?
What year do you have? I literally bought a cluster today out of the boneyard because the printed circuit was in perfect shape, and swapped it out with my cluster. I didn't use any of the gauges in it, so I have a spare slosh module and fuel gauge. But it is from an 87, so you might want to make 100% sure it will work in your car. I can't say for sure this one works, as I never plugged it into anything.
If someone knows how to test out a module and gauge, you can test yours and I can test my extra to make sure it works. If it does, I have no need for it.
