Sudden screen glitches & freezes, requiring force restart

Hello!

My 2012 MacBook Air (I have the 2.0 GHz dual i7 + 8 GB of RAM model) has, for the last few months, started crashing at random, requiring a force restart.

Out of nowhere, the screen gets glitchy ~ you can see what was there, but its colors & shapes distort. If any audio was playing, it also becomes just a glitchy (loud!) mess. The only solution is to hold down the power switch for 10 seconds and force a restart. Or sometimes it restarts on its own after a few seconds.

The troubleshooting I’ve done:

1) installed a clean OS (Mojave) on a separate partition. Still happens.

2) happens on both battery & two different AC power adapters.

3) happens with & without external peripherals connected (powered USB3 hub, audio interface connected via firewire-thunderbold adapter).

4) I’ve reset PRAM & SMC. No help.

5) happens under heavy & light workloads, even sometimes sitting idle (i’ll return to my desk to find it has restarted itself).

6) sprayed compressed air inside all vents in case something was blocked by dust causing overheating. No help.

7) Ran Repair Disk in Disk Utility after starting up from recovery partition. No results.

What I haven’t done: replace the battery, which reports “Replace Soon”. I don’t want to throw big money at the machine if its logic board is about to die.

Any thoughts? The machine (aside from random crashes) still suits my needs perfectly, and I’d really like to not have to replace it.

Thanks in advance!

~ Peter in Athens

Adding screenshots of CoconutBattery, per request!