Hopefully you just got a duff VSS. Not sure how the VSS drive works in the rear end, but in a FWD automatic Ford, the VSS mounts to the tranny and there's a plastic gear inside the tranny that drives the VSS. If that gear gets chewed up, the VSS will skip. A new VSS would work for a short time, but the tranny gear would probably cause a premature failure.
I'd remove the VSS and see if you can look inside and see the condition of the drive gear. Might have to use a mirror and a flashight. Maybe get a finger in there and feel around.
I'd also examine your new VSS carefully, not only for chewed gear teeth, but see if the gear spins too freely. A common fault is water gets inside, freeze, and pushes the electrical sensor up and the square shaft pops out of the VSS gear.
If you don't find anything obvious, maybe try a junkyard for a $5 VSS and see what happens. Having to buy another new one won't be much fun, especially if it's not the problem.
Here's one that failed from ice in a Ford Taurus:
Here's another pic showing all the parts: