Thanks for the picts. It does seem my shoulder was too long.
I got the replacement screws today that seem like ordinary screws with no shoulder. They fit completely tight without any wobble.
The bad screws turned out fortuitous. I had almost started cutting using the rail and bench dogs in my MFT3 top. I bought just the top and not the base. After the screws didn't fit I looked at more videos featuring the MFT3 table with the rails and guide, and saw it would really help me normal size pieces much faster than if I just had the dogs. The full table will also help me cut smaller pieces, whereas just the tabletop with dogs would have made that task difficult, always having to use scrap pieces on both sides of the rail.
So I saved the MFT3 top from getting any cuts in it and got the right tool.