I might be wrong, but a couple things jump out at me, and I'm hoping they are all mislabeling issues.
First off, the net labeled +5V is actually 3.3V correct?
Second, the microcontroller, CY8C4013SXI400 is a 1.8V microcontroller, not a 3.3V one... Might explain the half of the micros being dead thing...
Third, driving those n channel mosfets from an IO pin wouldn't work well. The Vgs ON for the DMG6968U-7 mosfets is around 4.5V, so if they turned on at all with a 3.3V microcontroller, they would be acting like resistors and dissipating lots of power (saturation region), meaning they would go over their power dissipation rating and blow up too.
To fix these issues, you would need to replace the AP2204K-3.3 with the AP2204K-1.8, and add a gate drive circuit for the mosfets.
did you check the data sheet for the correct part?
https://www.cypress.com/part/cy8c4013sxi-400it clearly states max operating voltage to be 5.5, not 1.8 or 3.3!
The DMG6869U-7 is also a logic fet, with only 36m\$\Omega\$ Rds
on at just 1.8 volts! clearly not acting like a resistor when driven from 5v!
https://www.diodes.com/assets/Datasheets/products_inactive_data/DS31738.pdfplease at least ensure that you're not spreading misinformation by reading the data sheets!
I have been looking over datasheets at DigiKey.. I found SSM3K2615R,LF and NVR5198NLT1G. They both have much higher Vds ratings and (I think) reasonable input capacitance and Rds values. I think either would be a better choice than my current - if you have a moment to look, I'd appreciate your feedback. On the schottky diodes for protection - I assume you mean putting the anode on ground and the cathode at the +14.5V at the top of the LED's? You mentioned diodeS, multiple, so do you also suggest adding one in the same configuration at points on the board, or is one for the whole circuit likely to be sufficient?
I had a look at the datasheets of the replacement fets which you found. both seem to have a bit too high of an Rds
on for what I'm used to with my own designs. I think the NDS355AN is a suitable choice in the SOT-23 form factor, but the FDS6930B is also a good choice and it's a dual mosfet package which makes your life easier. Psi mentioned some good parts too, use that TVS and 5V reg. you should select "automotive" parts rather than "catalog" when shopping for parts used in a similar project

T.I. often provides "military grade" parts too, in case you want to go overboard

to further reduce noise, you can use a pi LC filter (with the L, ideally being a common mode choke between + rail and GND rather than a simple inductor) like so:

(the choke is shown as two separate inductors here)
the schottky diodes I mentioned were for input protection, not for power lines. if you want something faster than transorbs (TVS diodes), you can use the BJT method which dave showed in this video (I recommend you do not delete the transorb, rather include both of these methods):
easiest way to ensure your inputs are protected, is to use a known clean input, like the output of the 5v regulator, instead of using voltage dividers directly from the battery!
I wanted to design a schematic to clean up yours, but the one you provided is very lacking. please provide the full schematic and we will clean it up a bit for you.