It doesn't sound like there's a problem with your 12V supply. The 12V supply is a bridge rectifier followed by a capacitor. It's unregulated and will drop in voltage as more current is pulled from the supply.
Some of the drop is due to resistive losses through the bridge.
Some is because the voltage at the output of the capacitor will droop at a faster rate when more current is pulled from the supply. As the AC input voltage is increasing, the rectifiers are forward biased and the capacitor charges up to the maximum input voltage. When the AC input voltage decreases from peak, the rectifiers cutoff the AC input and current is sourced from the capacitor. The causes the capacitor voltage to fall slowly as charge flows out of the capacitor. The rate at which it falls is proportional to the supplied current.
Without any mods connected, your 12V supply will normally be over 13.2V. As more mods are added, the DC voltage will start to fall. If you add too many mods, the voltage will fall below 12V and limit the amount of light coming out of the opto photodiodes.
As for your original question about why the flipper strength may feel weaker when the opto voltage is reduced... the detector side of the optical switch is a phototransistor. The current through the transistor depends on the light that reaches it from the photodiode. When the photodiode is lit brightly, the phototransistor turns all the way on and has a small voltage drop across it. When the light from the photodiode is reduced the phototransistor doesn't turn on as strongly and there's a larger voltage drop across it's terminals. The circuit that detects whether the flipper button is pressed or not depends on this voltage.