On boards like that last one pictured I use the "control room outs" even if one of the main outputs is available.
Was going to suggest this as well. Always with the clearance and cooperation of whoever is responsible for running sound. That provides the same mix as the Main Outs but allows you or the board-operator to set the level of the "control room out" as needed to your recorder, AND remain unchanged even if the main-out level to the PA gets adjusted before/during the performance. This is relatively simple and easy to do.
Another even simpler way to achieve that is to record via the headphone out, which should work fine, assuming it is not being used. This is often the best option if you are unsure how to work the mixer, and to minimize the burden on whoever is responsible for running sound.
To use the control room outs on that Mackie GigFX mixer you'd plug into the 1/4" output jacks marked "control room", and adjust level via the pot marked "control room" just above the (green) FX pot. You may also need to turn the "blend" pot just above that all the way counter-clockwise (to inputs) and maybe push the "to phones/cr" button located between the two. As long as you touch nothing else, nothing can potentially get screwed up by doing that.
On the Mackie 1402VLZ setting up the correct control room out routing is more complicated and could potentially screw up the main output. Tread carefully. Best to have whoever is responsible do it so that you don't screw it up.
On that small Tuga PR6X mixer there is no control room out. Easy to use the headphone out though.
The photo of the "full" board you show has a totally unused mono Aux 2 bus with all the mix knobs turned down. That could be employed to created a mono output mix in a pinch
This can be the best option, but is somewhat more complicated. Like the above options it also provides a separate output at whatever level you want, which can remain unchanged during the performance, BUT ALSO can be a mix that is different than what is sent to the Main Outs. Its more complicated because that mix needs to be dialed in separately, but advantageous in that it could contain whatever you want and not what you don't. It could for instance be only vocals, which might be the best way to go if you can't really listen to the mix while dialing it in (and is generally what you need most from a SBD feed). All of the above boards are capable of this, although if there are on-stage monitors in use for the band which are being by the AUX Send of the mixer, only the 1402VLZ has a second set that might remain available for this.
WITH THE TOTAL COOPERATION OF THE SOUND CREW
^Always!
