Hi Sander
First thing to try is a good star mask. You may just use the luminance to build it, with a touch of curves. HDRWT also may help to flatten other features, and leave only the stars.
Another thing to try is to expand the dynamic range. The downside is that you loose contrast/brightness, so you must perform new curves or histogram adjustments.
Anyway, indeed the stars blow out, and this happens with almost any high pass filter procedure. To have more control in ATWT with them, just select a peaked scale function.