I swear I was starting to doubt my sanity, at least now I know I'm not totally insane.
Your understanding shows that you have worked with scalars and know what happens when you operate mod n.

Now have you tried to work with target and it's 1/16? Try divide & add/sub scalar.
One thing I noticed, even if you post a private key of a funded address, not all but some people would ask what is this, what should we do with it?😂
And say how is that going to help us solve a puzzle, while they think finding a way to partially break ECC is like planning for a family picnic or throwing a dice and get lucky to land on a key just like that.

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To understand, you have to try any possibility until you find a solution, and since the group order is fixed, you can observe what happens when you divide different keys from different ranges, like sometimes you get 8 with some 0s after it, and when you divide by a larger number you'd get something like 67b with some trailing 0s, sometimes it goes like 8, c, 4, with trailing 0s.

You can understand what I say if you divide 0x1 by even or odd numbers, e.g, 2, 4, 6, 8 or 3, 5, 7 etc.

Something to work with:
Target: 1001, sub 200 to get 801, now if you divide 801 and 1001 by 200 you get 1, but do it using scalar, and set your range to 2:400, you will see 256 bit keys and in the middle only "1". Now how can we find an unknown key close to 200? And start by dividing and sub to land on one of the unknown key's divisor.

Let me explain, think of target as 1600, now if you divide and sub 1000 and 600, you'd get 400 being divided, now what if you work with 600 and 400, you'd get 200 divided, now imagine all the keys above are odd, how can we work with them by subtraction/addition only to get a composite number?