If updown was a special named dimension and you took a single 2-space+1-time slice of the universe at fixed radius from the Earth, your argument wouldn’t really be different, only words and phrases like “sitting still”, which is inherently about the dimension being removed, because it’s convenient for us.
And that’s ignoring questions like “can particles have momentum if there is no time?” which might actually be important in the unlikely event that I understand what a black hole’s singularly does to time.
Regarding the last question, if I understood forces correctly, it's that they remain in motion until an equal or greater force stops them right? Why do we need time for that out of curiosity?
Momentum has a direct influence on Einstein field equations, and I don’t know enough maths to follow GR (just two A-levels) so I have no idea if that “direct” influence is still present at a no-more-future boundary condition.
My insufficient maths skills are, amongst other things, why I don’t trust my understanding that a black hole singularity really is a no-more-future boundary condition.
A fascinating book on this topic is "Philosophy in the Flesh" by George Lakoff:
I don't believe that mental experiment proves what you think. If you freeze time, there wouldn't be anyone that could make observations. You might as well choose one fixed point in the universe, eliminating space considerations, and think about its whole story from the beginning to the end of time; that would be as real as a frozen universe.
I think of reality as a goo of vibrating stuff, encompassing all matter and energy. Matter creates space, and the vibrations of change create time.