Given how expensive this computation would have been in 1997, it makes perfect sense they'd taken months, but even if we assume they tried all timestamps of 1997 and selected arbitrarily among the first 16 viable candidate of any timestamp, that's just ~30 bits of freedom.

Finding out there is a class of weak 256-bit elliptic curves so large that they can be hit randomly with 2^30 tries would be a cryptanalytic breakthrough analogous to discovering all elliptic curve cryptography is broken.

Read section 3.1 of the Koblitz and Menezes paper. It was already implausible with 160 bits of freedom. https://eprint.iacr.org/2015/1018

If you want to believe the NSA knows ECC is broken and chose to risk moving the US government to it and somehow no one figured out the same break in 30 years, you're free to do so. But pretending the seed choice plays any role in that theory is over.

"..chose to risk moving the US government to it.."

Oof, about that...

As a complete layman, I do wonder why n grows with each subsequent curve, rather than with number of bits. Does this not suggest they were 'searching harder'?

>they can be hit randomly with 2^30 tries

More precisely: not very random tries.