You know, I read your first post and at that particular moment I didn't have the 30 minutes to post schematics and troubleshooting thoughts. And I was feeling a little bad about that but you managed to solve it yourself in about 3 hours, which is remarkable. I don't know if your post is allowed either, but it's an easy mod to describe. Pull the module out of the gauge cluster and view it T shape up and components facing you. You will see a row of contact strips, 3 to the left of the latch and 2 to the right of the latch. Use needlenose pliers to strip out the left three contact strips. Then solder a small length of wire to create a short across the two right contact strips. I have not done this myself, but that is what the referenced article shows.
I'll add this, now that I have seen a picture of the slosh module internals: It's a pretty basic circuit consisting of a standard op-amp chip and some stock support parts. I think if I had one of these in my hand I would first of all clean the contacts on the module and the corresponding contacts in the gauge module and see if that fixed it. If not, I would look at the back circuit side for anything suspicious like corrosion byproducts or cracked solder joints. If all of that was ok, I would replacing just the electrolytic capacitor which is the largest part on the board at the top of the T. I think a lot of people here know electrolytic capacitors have a limited lifespan. Other than that, there's a handful of common diodes and resistors, plus the op-amp chip. If you have a friend that dabbles in electronics, they could help you test the parts or you could just have them replace all the parts. That may sound extreme but all the parts put together would cost maybe $10. But I figure it's going to be most likely the contacts, some corrosion somewhere or the capacitor, 9 times out of 10.
Or you could just do the contact modification and call it a day. The only by-product, as one might guess is that the fuel gauge will jump a bit but it should be steady and reliable while you are sitting or driving straight at a constant speed.