how to calculate the gain of this? i started drawing the circuit on circuitlab.com and they paywalled me!! i would prefer to improve my generalized knowledge and intuition of how it works rather than to just calculate it.

U20 and U21 are cross-coupled (servo-balanced) and the point is that you can connect it unbalanced with one output pin shorted to ground and the gain on the remaining output pin will be doubled to compensate. i don't get the mechanism of how it gets doubled.

is there any particular reason for why (like DC offset of the U20 and U21 NE5534 op-amps) you would not want the circuit to be like on page 12 here so that the inverting U19 TL074 can be skipped:
https://hparchive.com/Journals/HPJ-1980-08.pdf