The top cap acts as a washer of sorts, so without it it's not surprising the bolt is loose since it is not screwing down against any resistance. Also, many top caps are domed, so I'm not sure how it can be determined to be "too high" without a top cap in place.

Get the new top cap, install it and go from there.

Edit:. Once you get the headset preload set (the primary role of the plug) and the stem correctly tightened, the star nut/compression plug really doesn't have a mechanical role in actual use (although the plug helps to protect a carbon steerer from stem clamping damage).