The design for the rectifier is rather clever, and comes from TI's TIDU030: Precision Full-Wave Rectifier, Dual-Supply.
It looks as follows:
simulate this circuit– Schematic created using CircuitLab
R2=R3=R4, and this rectifier has gain of +/-1. The architecture is nice as it keeps both op-amps operating closed-loop, without saturation. D1 and D2 can be Schottky microwave RF diodes to lower crossover distortion.
Could it be made to have inherent gain greater than 1? It's not as simple as changing the R3/R2 ratio, since the gain for the positive input would still remain +1.