Here's my fix for the blown BQ24074 battery management chip. I planned to supply 3.3V to the board using a Buck DC-DC converter, but I knew I had to disconnect or remove the bad BQ24074 first. I also knew that would be difficult. Well, it was much harder than I expected to remove the tiny surface mounted chip. It would have been even harder to cut the offending trace. In any case, I managed to cut it out as you can see from this photo.
The orange wire is the voltage source going to the DC-DC converter. I connected it at the cathode junction of CR6 and CR7. That way it will convert either 5V coming in from the USB OTG or 7-15V coming in on J21.
The next photo shows the converter on the underside. The green wire is the converter's output and goes to J20-1 or V_SYS. I also have it connected to J2-1 so that a 3.7V LiPo battery can also provide power to the Edison module. The only downside to this fix is I no longer have a way to charge the LiPo with the breakout board. But that's OK. I have other ways to charge it back up. An advantage is I can now supply the board 5V up to 36V on J21 instead of just 7-15V.
I can't recommend this fix to anyone unless they are willing to take a high risk of ruining their board. It is extremely difficult to remove the chip and its 17 miniscule connections. BTW, Intel did offer to replace my board, but it was going to be 6-8 weeks before they had warranty stock.