Interesting thought experiment.
I did some calculations to help visualize the size of puzzle 67's keyspace. There are 73786976294838206464 possible keys in puzzle 67. Some may look at the number "73786976294838206464" or at the hex range of 40000000000000000:7FFFFFFFFFFFFFFFF and think, well that number doesn't really look that big.

Now let's take a look at the Great Pyramid of Giza, in Egypt. It is the largest pyramid in Egypt, with an original height of around 146.6 meters (480.6 feet) and a base length of about 230.4 meters (756 feet) on each side. Next, imagine you have 73786976294838206463 grains of just average, white, sand, and just 1 grain of black sand (representing all of puzzle 67's possible keys, and the 1 private key). You would fill the volume of the Great Pyramid of Giza with sand ~370 times. Try to picture 370 of these pyramids, all of white sand, and inside one of them somewhere is 1 individual grain of black sand.

If you took a typical US 5 Gallon bucket, and could check 1 bucket per second, looking for that 1 black grain of sand (and hopefully not miss it), that's about 1.5 billion grains of sand per second. It would take you 1560 years to check all of the sand, assuming you were checking nonstop, 24/7/365. Maybe a little bit longer, if you took a few breaks to eat some yogurt.