That's exactly it!
Yes.1. Is it necessary that the compression portion of the BA5A be balanced?
Yes.If so I imagine that it is to avoid thumping
More or less correct.but I would not think that a little AC feedback applied gently to the cathode of a tube would make it thump.
Instead of jerking the grid voltage with a few dozen volts, it jerks the cathode current in a way that produces similar thumps. Actually, the goal of the topology is to minimize thumps, goal achieved.We aren't jerking the bias point around like in a varimu, just cancelling some G-K potential.
It's a feed-forward compressor with pre-delay. The control voltage is taken pre-delay.2. Why is the control voltage sampled from the input side of the circuit. Wouldn't taking it from the output make more sense?
Because the designer thought it was the best way to insert delay and attenuation.3. Why the two nearly back-to-back transformers?
Several misconceptions and misunderstandings in the various comments.Copy of GE spec sheet with GR curve
https://www.preservationsound.com/2011/05/pro-audio-hardware-of-the-early-1950s/
Read comments at end, good description of the HF phase time delay network and reasoning behind it