@barryjump The board has finally arrived - and after wrestling it out of the hands of customs with the usual fine and fees - I finally got it in my hands! 
I got my own/known good balenaFin 1.1.1, plugged out the CM3L+ module and started measuring power draw by using an DPS5005, outputting 12V, with a max current of 1A, “trigger happy” with my thumb on the cut-off switch (not yet needed, but… preparing ;)). Then I measured the power with the CM3.
Then we needed to get to work on the real thing: I popped out the CM3 from @barryjump s poor fin, plugged it in - and saw similar “at rest” current draw. Thats a good thing. Then I popped in the CM3 - the values were all over the bench, but nothing too shocking or exceding the maximum values I saw earlier. But also, as he reported - the LEDs stayed in the “broken” state. Well.
Now was my decision point - what did I trust more? Putting in the “cursed” CM3 module into my fin - or my CM3 into the “cursed” fin? I opted for the second option, putting in my CM3 into the broken fin - powering it on - the power stayed ok, but the LEDs stayed the same. I had a bad feeling. I put in my CM3 into my fin - and was relieved to see it still worked. Ok. It looks like the fin is really toast… so… is there any hope for the CM3? Only one way to find out - putting it into my fin - and nice! It booted!
Ok, the CM3 is ok - the fin is not? Well… I got another idea: I put the “fryed” fin and the “uncursed” CM3 on my PC, started balenaEtcher…
Well, the Sandisk eMMC is fryed! Thats the reason, its the same as with Failing FIN boards and Damaged Fin after power supply failure
So to wrap it up - the CM3 is fine, the balenaFin itself probably too, but the eMMC module on the balenaFin is fryed. I tried multiple rpiboot hacks, mounting it to the pc, trying to low level format it, erasing partitions, rewriting, overwriting with rufus etc - nothing worked sadly. Maybe @hraftery or @ntzovanis have an idea? (I can try to play along with recovery tests. Maybe there is some kind of code that could be run via rpiboot to really low level format the eMMC and getting it working again, other than only trying this via the filesystem mount?)