So yeah, I've been obsessed with making rigs battery-powered and/or fully wireless for about 20 years now. (This all started with laptop builds, which include rechargeable batteries pretty much by definition.)
My approach with my recent QC build was to simply find a laptop battery charger with suitable outputs. This one is, sadly, no longer available, but I imagine there is an equivalent or better by this point:
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The QC is unusual in that it demands 12V rather than 9V. This supply provides that voltage, on its own dedicated barrel jack connector, at up to 3A. So all I need is one (polarity-inverting) cable from the battery to the QC, and I can use the battery's soft power switch to power up and down. I tested the board when I first built it and it ran something crazy, like 17 or 18 hours, on one charge. Plus you can charge the battery while the battery is running the QC without taking anything apart. Very convenient.
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