Lets model that twisted pair, assuming VERY SLOW RATE OF TWIST, as 2 wires of spacing 4mm (these are power wires, after all) with distance 100mm and 104mm from the vulnerable sensitive PCB loop of area 1cm by 4cm. We'll compute the induced voltage for distance 100mm and for 104mm, then subtract those for the presumed magnetically-induced trash in the sensitive circuit. We'll also need the slewrate of the power line currents; we'll assume the rectified diode peak currents: 15amps * 10X, and 1microsecond turnon time, to be the aggressor Hfield.
Math: Vinduce = [MU0 * MUr * Area / (2 * Pi * Distance)] * dI/dT
and inserting MU0 = 4 * pi * 1e-7, MUr = 1, we get the form
Vinduce = 2e-7 * Area/Distance * dI/dT
Vinduce = 2e-7Henry/meter * 1cm * 4cm /100mm * 150amps/1uS
Vinduce = 2e-7 * 0.0004 meter^2 / 0.1 meter * 150e^ Amps/second
Vinduce = 2e-7 * 0.004 * 150 e+6 = 2e-7 * 0.6e+6 = 1.2 e-1 = 0.12 volts
for the 100mm distance.
For 104mm distance (the other wire of the twisted pair), the voltage is 4% lower; our residual voltage from the twisted pair is 4% of 0.12 volts, or 5 milliVolts.
Can your precision sensitive circuits tolerate 5 milliVolts of trash, with fundamental repetition of 120 Hz, with a few microseconds duration and 1uS risetime?
How to mitigate this 5,000 microVolts of trash? We have all the degrees of freedom specified in the math: loop area, distance, dI/dT, and the UNSPECIFIED
variables of (1) how tightly the twisted pair is twisted and (2) how uniformly are the twists. You can measure these effects in the lab. Make a loop of 1cm by 4cm (or your personal choice of loop area), and measure Vinduce for various sinusoidal drives (with 50 ohm resistor to avoid shorting the Function Gen), with untwisted wires, human-twisted (non-uniform) wires, and machine-twisted wiring.
Note the skin depth of copper at 60Hz is 8 millimeters, at 60MHz is 1,000X smaller at 8 microns (1/3 mil or 0.0003 inches), and at 6MHz that skin depth is 8micron * sqrt(10) = 25 microns, compared to 1 ounce/foot^2 foil of 35 (3-5) micron thickness.
Your 1microsecond Trise has period of 2uS, or 500,000Hz (if this is valid way to model a quick Trise with very slow 120hz repetition). Skin Depth of 500Khz is about 80 microns of Copper. You may want a steel tube around the power lines, or route the power lines through a steel trough.
Should you decide to NOT USE TWISTED PAIRS, but use separate (color-coded?) wiring for 117vac, there is nothing to hold those wires at 4mm spacing, and your induced voltage can easily double or triple, to 10 or 15 milliVolts.
EDIT#3 April 2020
You will notice a big reduction in coupling, if the rate-of-twist is fast (many twists per inch) and the twisting is done by machine (so the magnetic field variations are very regular and thus mostly self-cancelling).