Early 2014 MacBook Air Random Shutdowns

Hi all, I wonder if anyone can please offer me any assistance.

I've been having a lot of trouble with my Early 2014 MBA and random shutdowns. It started right after I installed Big Sur. The symptoms are:

1. Occasionally, MBA won't turn on at all. When it does (Apple Logo and Start sound) it will shutdown.
2. If it does start, it will seem to be all fine and then randomly turn off. There is no apparent reason for it (no specific pattern, applications etc...).

I've done extensive research online, including on this forum, but can't find a solution. I have tried lots of things and whilst it does seem to be much better now, I may be tempting fate and I fear it may do the same again soon. That said, the only major symptom at this time is that the laptop takes a while to 'get going' and eventually starts after 3-4 attempts (Apple logo and then random shutdown a few times and then a normal boot).

Only error logged for shutdown cause is (occasionally - not all the time) 'Previous Shutdown Cause' -128 (Non specific hardware).

Here's what I've done/checked:

• Full system wipe and restore to fresh and clean install of Catalina (Downgrade from Big Sur).
• Disabled AppleThunderboltNHI.kext. Csrutil enabled and disabled, no difference.
• Apple Hardware Test pass with a couple of minor exceptions.
• Etrecheck Pass (No major issues other than 'Your machine is obsolete').
• CPU - Load Testing Completed and successful with temperature okay. This (to me) rules out Logic board as system is working but intermittent when starting up. Replaced Thermal Paste.
• Battery - Replaced with new - Correct Performance.
• GPU - As with CPU, Thermal Paste replaced and heatsink inspected - passed.
• Fan - Is working, heatsink is working however, fan is suspect.  Possibly overheat on startup causing shutdown. Not 100% sure if fan is running on start every time (it does seem to jam occasionally). Manually set to run in certain temperature range and it does work.
• Memory - seems okay and passes memory tests including Memtest (Rember) and Apple Hardware Test. Reset countless times.
• SSD - Working and correct, repaired with first aid and recently reformatted and fresh Catalina install.
• Power Adaptor - Seems fine but could be suspect MagSafe charger shorting due to minor cosmetic damage.
• Physically cleaned the system inside and out.
• Apple SMC - Has been reset countless times.  Appears to be working normally.  Has latest firmware installed.
• Tried disabling Sleep.
• Tried running various 'NoCrashMBP'-type scripts and automator scripts as recommended online - no difference. Although, to be fair, I haven't actually tried NoCrashMBP itself (don't want to pay $10!).
• There's no third party apps running in the background.

I'm truly out of ideas but, as I said, it does appear to be working at the moment except the fact it currently takes a few attempts to switch on...

Any ideas or anything that others have tried for a similar model? I'm not getting it serviced and don't intend on buying a new logic board but any suggestions would be very much appreciated. Thanks very much!