Identifying an unknown Android tablet through adb/shell without relying on build.prop I obtained a cheap unbranded tablet from a friend, without a box or anything and I need to figure out what kind of tablet it is, through software. 

What I've established so far is that the tablet is an Alwinner A13, but unfortunately there are a lot of A13s and this one seems to require some non-standard touchscreen drivers. 

There are a few more threads about identifying devices, but this case is slightly different, in that I can't trust anything Android tells me about the tablet. 
The tablet is currently running the official Novo 7 Legend firmware, which "works" but unfortunately is not the right firmware for the device. I still have full access to the system over adb and with a mouse over OTG, however the device's build.prop is wrong. 
Unfortunately build.prop is also what defines the tablet's type/name in the Android "About device" section and all Android log output I've found. 

I've checked dmesg as well as the output of adb bugreport, neither gave me what I'm looking for.

tl;dr: 
I do not have the original firmware nor do I have the box and the hardware is very generic, so my question is, is there any (software-wise) way of identifying the tablet, that does not rely on build.prop?

I have full (root) adb access and full access to Android.

Update: I have opened up the tablet and checked the board (and lost the power button in the process), on it was a more specific name, but still very generic. I did manage to get some rom working on it thanks to it (albeit with an inverted touchscreen), but I still haven't been able to identify it. I've given up on it for now (I got it for tinkering purposes anyway), if I get new suggestions here I'm still more than happy to try them out however.
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.