Moving a smart shape to a new note is easy. Click and drag the handle for the start of the slur and drag it to a new note. The new note will be highlighted verifying the attachment. Do the same thing with the end handle of the slur.
It might be faster to just delete the old slur and out a new one in at you desired location.
If you're trying to do this where the slur starts on one system and ends on a different system, the method is a little different. The easiest way to do this is to switch to scroll view, change or re-position your slur, then switch back to page view.
With some Finale options the order in which you select things make a difference. Try an experiment...
Choose the articulation and release.
Then press and hold the ALT/OPT key
With the OPT key held, click and drag the articulation and see if the anchor line says fixed.
There may be simpler ways to do this which you can find by trial and error, but this seems the most reliable way I have found to move one staff with the Staff Tool, so I thought I'd suggest you try it with articulations.
I'm working with support on this as well They wrote:
" since there typically isn't a use case for providing a different set of instructions to the player (in the part) than the conductor (in the score)."
It's not at all about giving different instructions. It's only about layout. The lines in the part have a completely different layout than in the score.
In the first screenshot, you can see a bit of the attachment line slanting upward to the right. That line attaches all the way to the previous staff last bar. So, although the line is attached to the previous system, Finale is drawing it on the next staff.
In the next screenshot, You can see that the rit..... line does not continue on the next staff the way it should.
If I move the last bar of that staff to the next staff, then there is no rit.... line at all! (See the last screenshot attached)
So I need to move the rit... line in the part to work around Finale's problems displaying the rit... line correctly.