Regardless of how the voltage is lowered, you aren't delivering the power to the heating elements that they are designed to deliver. For a resistive heater, the power scales with the square of the voltage.
Delivering 11.4 V to the heaters will result in the power being $11.4^2/12.0^2 = 0.9025$ or 90 % of the intended power.
There are two things you could do to increase the power at the heaters.
- Your voltage is starting out low, which you may be able to increase
at the power supply to 12.0 V.
- The voltage drop in the 1-meter cables can be reduced by using
shorter cables or larger cross-sectional area conductors. 13 gauge
is not a very heavy wire for low-voltage high-current DC. I would
suggest 10 gauge, and would prefer 8 gauge.
The logic in the controller board should be fine as you are now. Controller boards include regulators that being the nominal 12 V down to the 5 V or 3.3 V required by the digital logic. These will automatically adjust for changes in the 12 V supply.
To actually answer your question, the permitted voltage drop is application dependent. As a rule, though, I would suggest that the voltage on the pins of the controller should be 12 ± 5 %, or from 12.6 V to 11.4 V. The voltage you measured should be acceptable if it is the true minimum voltage.