I would like to set the value of a number slider, directly via the grasshopper script components (C# or VB), so that the new slider value can be used in any component that uses that value as an input.
In other words, does anybody know a way to manipulate sliders via scripting?
Bad idea. When you change a slider position during a solution (which is always the case if you're doing it from within a Script component) then it will wipe out half the completed solution.
You should only change the state of a network after a solution completes and before the next one begins. I.e. you can do it from a dialog box, or via some sort of event handler, but not from within RunScript() or SolveInstance().