Make sure you watch the section about power distribution in this video. The power distribution part starts at 5:59.
I don’t know what sort of power distribution boards are available for this sort of stuff but I’ve made a few of my own power distribution boards for my robots. Here’s one design which excludes the solder mask on the bottom of the power line of the PCB. This lets you add a layer of solder to allow even more current to flow without heating up the board.
The signal lines can connect to the 2x5 header on the left (looking from the top) I often use ribbon cable to make this connection.
Here’s a link to the zipped Gerber files for the board above. If you submit this zip file to OSHPark, they’ll make you a set of 3 for $5.
Here’s a photo of an older servo power board I made.
While I used a ribbon cable in this situation, I often just use separate wires as well.
These sorts of boards are easy to DIY using some perf board. Here’s an earlier version made from perf board.
I’m new to all things Pixhawk so there may be plenty of other solutions which I am not aware. I just thought I’d share some of my experiences using lots of servos.