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However, I was wondering if there was a less intrusive solution, like using another pin somewhere on the board which is accessible and can be enabled in the firmware accordingly.
Sure, do this. While PWM-able pins are prefered, any digital I/O pin will work. Most firmwares don't do PWM on the heated bed anyways.
Regarding which pin exactly ... well, you have the board in front of you, so you can look at it much better than me :-)