This project was delayed by other priorities for more than 3 weeks. I decided that the most prudent way to proceed was to just populate the BAT1 channel and the 5V regulator to see if the charger complained about anything when I tried to charge a battery. Before connecting a battery,  I measured some voltages at the gates of the balance lead FETs, the charger input, and the voltage drop across M1 (the ideal diode PFET). All the voltages appeared to be correct, and the drop across M1 was only 25mV with a 2.5A load current (that's 10mOhm.) I also applied >25V at the battery and balance leads to make sure they were capable of 6S LiPo voltages.

The charger (a SkyRC Q200) did not complain and proceeded to charge the battery (a 1.6Ah/3S LiPo) without issue. 

Then I populated all of the PCB and began testing the parallel charging function. I was not very rigorous about this testing. Basically, I just attached BAT1 and BAT2 and started the charger. When the green light lit I checked the cell voltages to see if there were any outliers. I did the same thing when adding BAT3 and BAT4. After all of the batteries were in place and the MATCH LED was lit, I stopped the charger and reset the charger current to 4X the battery Ah, which in this case was 6.4A. This channel of the charger was limited to 50W, so I could only get 4.2A from the charger at 12V output.

I swapped out the 3S batteries for 4 850mAh 4S LiPos. I charged these batteries from about 3.8V/cell to completion -- it took 35 minutes. I immediately checked all of the batteries using the battery meter function of the charger:

BAT1 - 16.78V (4.19, 4.20, 4.18, 4.20)

BAT2 - 16.77V (4.19, 4.20, 4.18, 4.20)

BAT3 - 16.76V (4.19, 4.19, 4.18, 4.20)

BAT4 - 16.77V (4.19, 4.19, 4.18, 4.20)

The batteries are within +/- 10mV, which is a pretty good result (though I'm not sure that the charger or parallel station had anything to do with that result.)

The only "glitch" that I noticed was that the charger would complain about a reverse battery insertion when I unplugged the last battery from the parallel station. That may be a result of the balance leads not grounded on the parallel station board -- I did not want any ground loops.

I also tested it with an old SkyRC B6 charger (50W single battery charger) and it worked just fine.

Conclusions:

As far as I can tell, after some pretty basic testing, it works as intended. After playing with it for a couple of days I have a list of small changes:

1. Add LEDs on each battery channel to indicate how many batteries are matching so the user can increase the charging current to speed up the process, if desired.
2. Add resistors to the balance lead grounds to possibly prevent the complaint from the charger about reverse voltage.
3. Both right-angle XT-60 connectors had to be placed on the bottom of the board because I got the connectivity wrong. If there is a revision, this should be corrected.
4. Make some right-angle XT60 to XT30 adapters to allow for some more room when charging LiPos with short leads intended for quad copters.