Dear Paul,

since July I am experiencing the same problems with my custom project: I connect a new Overo Fire on my custom made board
and after a few days it stops working, sinking about 5 ampere from switching power supply: this way, I burned 3 overo fire extended,
experiencing the same symptoms you have.

I designed and assembled the custom board; each time I start working on it, I check that there are no short circuit between ground
and all the supplies I have all around the board (3.7, 2.8, 1.8).

As main power supply I used the 3.7V coming from lab switching power supply.

When all the incident occurred, I saw that the 1.8V linear power supply was boiling hot, and after incident was not working anymore.

For the execution of next tests, which I will experience until I burn my last two overo (and after I will stop it) I am going to use 3.7V
coming directly from a li-ion battery, I will use solder paste stencil, in order to produce cleaner parts, and I will not connect any
other peripherals (in fact, I burned also two gprs modem).

Tomorrow I will post my overo connection schematic. The only difference I saw between main and your schematic, gpio apart, is
I connected VBACKUP and AGND to ground.

At the moment, total damages is about at 1000 euros, and I do not know who I could ask for support.

Hope you will solve your problem.
bye
-g