Cool video. Just one point though, the combined gain isn't ß², it's ß1•ß2 where ß1 and ß2 are the gains of the 'driver' and 'output' transistors respectively. So if the 'driver' has a gain of 100 and the 'output' a gain of 50 (a common situation in audio power amplifier output stages) you'd have an open loop output stage gain of 5000.