Hi @walcott,
I’ve had a look at their website and it does look as though the HAT would work perfectly fine with the pi-top [4]. I’d be very interested if you got it to work, so please go ahead and try. We designed the pins on the top to supply more than enough voltage for something like this. If your pi-top were to somehow break then I’d be more than happy to send you a new one for free.
We also have two of these cells inside the pi-top [4]. The power for the HAT can be drawn from these cells by connecting to VSYS_OUT on our modular connector - You can find the pinout here. Please be aware that VSYS voltage is dependent on the type of USB-C power supply connected: the pi-top will always call for 12 Volts if the power supply can give it, but will also accept 15 Volts at a lower priority. If there is no power supply connected, then VSYS_OUT will be the battery voltage (ranging from 8.4- 3.7 Volts).
If you’re serious about getting this all connected let me know and I can offer an Expansion Plate to you at 20% discount and you would be able to solder wires to the plate for the power to your HAT.
Anything for more projects! Good luck and do share any progress you make