Ok, so what does the stack height do? Looking at my other bikes, technically it could affect the ride height if the height on the bottom part is differrent. Otherwise, it looks like it's just the height of the stack of spacers, adjuster and locknut on the top?
This looks like it shouldn't be too hard to deal with. Just a matter of measuring the head tube and making sure the cups are the right diameter.
Total stack height
is the measure to often just under the top lip of the fully assembled top and bottom in the frame. As your frames headtube is fixed, this is just added to the headset stack height. You need to cut your steerer tube to that height. Some headsets may have a variable stack height built in, (notably mavic from bitd (late80/early90) for their mtb, road probably the same and doubtless other road are similar)
Sometimes you can pack the top lock nut upward with spacer in between it and the cup, it depends on the design.
If your steerer is already cut to a lenght, you cannot fit a 'taller' headset as there will be nothing there for the lock nut to screw on to. Look for a different one.
While not going into great details of old headsets (try sheldon brown website ) Sutherland 7th headset section has some nice diagrams