On the naming of points:

I think what you really have here is a banking system. Soft points are just points. Hard points are points that are protected. The most common term that comes to mind for protecting a point is to Bank it.

Now what the final term is depends on how the theme is presented theme. I think you could keep the term points, but you might also refer to points as code, gears or cogs.

Banking them would then be something like hardcoding them or compiling them.