I was going to suggest using pneumatic cylinders and some small rail sections to extend your pick and place and solder dispenser when needed so that they were below your spindle bit, and retract them when not. That way the same screw driving the spindle could also drive those 2. However, this seems about the same complexity as having 2 extra screws and requires an air source, so probably not what you're looking for.
You could have manual clamps on the solder dispenser and pick and place that have their own short linear rail sections and that way they could be driven by the same screw and not have to be removable.
I found this pic online, but I've seen them before, they can be found in a number of varieties. I'm guessing you could even make some from inexpensive MGN12 linear rail parts.
I found this on YouTube and find it interesting the way the pick and place rotates the part and the X Y zeros are set.
Good Luck!
https://www.youtube.com/watch?v=CRSLbo_8nTQ