My 4" Abwood dismantles just as you have tried. The leadscrew comes out with no difficulty. To remove the moving jaw from the dovetail slide, it's necessary to remove the jaw-plate, really needs a short or a cranked screw-driver.
If you did this, you might be able to slide the jaw back far enough to reveal the tee-nut, I'm wondering if you have something like a circlip on the end of the screw to prevent it coming out of the nut.
Again, on mine the nut is held by a countersunk screw visible on the under-side in the middle hole of the 3 you appear to have on yours.
Hope that helps.