Identifying an unknown Android tablet through adb/shell without relying on build.prop
Have you tried these:

adb shell getprop ro.product.device
adb shell getprop ro.product.model
adb shell getprop ro.product.name


EDIT: Upon re-reading the question, it seems that my suggestion is not applicable.
I trust that you have a stock recovery? If so, connect it to PC while in recovery mode and do the following over ADB:

adb shell
cat default.prop


If default.prop still does not give you what you want, I'm really sorry but I can't think of any other solution than to look for a stock firmware.