So here is the new base (v 2.1), I made it so that the base will fit over and swallow the stump of the hand pusher tool (or at least my clone of the tool), I also reduced the OD of the bottom skirt a little as it looked/felt a little large, here are a few pictures and the fake .pdf file which you need to convert to .zip once downloaded.
The cut-out seen on the below image on the bottom of the base should swallow the OD (40 mm, +0.1 mm tolerance) of the stump and the height of the stump 9.5mm (measured to 9.1mm, but rounded to 9.5mm) - let me know if this works for your tool.
Note, I think you may need to print supports for the new internal shelf created?
Here is the fake .pdf for just the FreeCAD base file and 3mf files
Modular Movement Holder.pdf
Here is the fake pdf for complete set of the new base and ring FreeCAD/3mf files:
Modular Movement Holder base and ring v 2.1.pdf
However, I'm wondering how often you could use this feature, adding the dial usually increases the OD of the movement, so you would need a new (larger) adapter ring tuned to the OD of the dial and I wouldn't like to grip the dial in any kind of movement holder if It could be avoided for fear of damaging it. Maybe I'm misunderstanding you?