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Can't. You need a real earth, with an atmosphere, about 230,000 kms from the moon.
You'd do better to rely on some decent photos others have taken during real lunar eclipses; some do show a few stars.
A large part of your problem stems from the extreme range of illuminations involved. Prior to the penumbral phase the moon is 100% fully illuminated and the backreflectance is high, making it a bit brighter than an "ordinary" full moon, and in a decent photo of this there is NO chance whatsoever of recording any stars.
As it goes into the umbra the illumination drops by many orders of magnitude to the extent that while fully eclipsed you can photograph magnitude 6 stars in close proximity to the Moon. Between 100% full and fully eclipsed the change in brightness easily exceeds the dynamic range of digital cameras.
Lastly, the reason I suggest you need a real earth to do this is the effect of the atmosphere which scatters reddish light into the earths shadow, causing the colours we see in a real lunar eclipse. Short of using a real photo I don't see how you can simulate this with a crude mechanical mockup.
It can be simulated in computer software fairly well, though most of the simulations I have seen were based on real eclipse photos.
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