I have done many of these, and, I have found it to be better to remove the NES power/av/rf unit by opening up the RF unit and desoldering it on the RF unit's solder side, versus flipping the NES motherboard over and desoldering the pins from its solder side. There is a risk of doing it the latter way, in that it is easy to damage the through holes and traces on the motherboard if done on that side. You then remove the solder from the 3-4 attachment points that connect the AV/POWER/RF unit's chassis to the mainboard.
The board isn't burned -- that's the 30+ year old nasty rosin core flux all these vintage consoles and such used. If you open up any of these old consoles, you will see that there's brown residue all over the place where any RF shielding is connected to the motherboard. Reheating it at 350C makes it spread everywhere. It will be cleaned off completely prior to replacing the capacitors, rectifier diodes, and voltage regulator in the RF unit, and the caps on the motherboard.
Here is a link to the video