As requested, fire test results night.

A little overdue, but tonight was cold enough at home to light up the fire and put in the test piece.

The fire, coal at its base, a mix of softwoods above.
The test piece is in centrally and the fire was kept fuelled at a level similar to what's pictured above for roughly 3 hours. When adding new logs the metal could be seen to be glowing orange/red.

End of the evening, metal cooled slowly.

Lightly brushed (dry) to remove soot. Some letters obscured.

Next cleaned with a mild abrasive (plastic dish sponge and water).

First observation - The heat of the fire appears to have melted the copper. The copper was the decorative plating added to the bitcoin logo and lightly to the lettering. The now seems to be the orange splodge in the middle of the card. A google of coppers melting point puts that at 1,085'C. A search for typical fireplace temps ball park figures depending on fuels for anything between 800'c to the max theoretical adiabatic flame being 1977'C.
According to
http://www.doctorfire.com/flametmp.html a typical house fire reaches as sustains around 1097'C. More to read there if you're interested.
Lettering now is readable with just 4 of the characters in the private key obscured beyond certain readability. An 'E' could be an 'F' in the end of the top row and the 'v' at that point was now readable.
So I moved on....

These last two pictures are after a clean/light scrub with "Brasso" metal polish. I'm sure any light abrasive cleaning fluid would do.
This made a huge difference and removed a lot of debris from the fire. All letters a lot clearer now.

It's tricky to photograph but I assure you the private key was then legible with then just 2 characters requiring some time/interrogation to confirm.
Where to go from here -If the purpose of making these was purely for function then I don't recommend the decorative copper plating on the logo/text. Coppers melting point is too low for this task. It may also cause issues in several year with corrosion on it's own or though the effect of dissimilar metal corrosion. The stainless steel card handled the heat very well. There is a slight deformity in the centre of the card. Perhaps 5mm in length, a slight shallow dent. I suspect the metal may have softened slightly in the heat and the addition of a weighty log may have caused it.
I would, in my next test, etch slightly deeper to aid in the reading of the text.
But to conclude I regard the prototype a success and it performed it's purpose. For a homemade DIY project that has sat at around 1000'C for the past 3 hours it's handled it well. That test piece was only the second I've ever made and I'm certain my next will be significantly better with those improvements.
I hope this helps and I'm happy to answer any questions about this, or to help someone with anything regarding giving this a go for themselves.