I see - we are redesigning a website and the client uses this for their headlines - the X-height on a standard small cap is too low makes it seem awkward. Small-cap in CSS is even smaller than that.
you might just have to make them as images & customize the x height from software. indesign is a simple preference setting. i think standard is 70%. of course, opentype is a whole different story as it carries its own idea of what to do.