The goal is to find some key, it doesn't matter if it is invalid for the bitcoin standard, because knowing the pk of any of them will know the original pk you are looking for. If you limit your mind thinking about the parameters that satoshi imposed, you will not achieve
example: suppose you want to find an unknown key that we call Z Z= 1200 if we know that its range is between 1000:2000 if we subtract 2000 we will get -800 wow yes, an invalid key?? should i care The answer is no, because if we find the value -800, even if it represents an invalid key, we will know that the original pk is 1200.
Ok, how do you know the result is -800? And whatever the result, it's not invalid, but what if the key is 1890? You'd be searching from 700 to 800 in hopes of finding you imaginary -800, while the actual result is 110, far away from your searching range. I guess you haven't figured out a way to validate whether your target is greater than 1500 or not, once you figure that out, you can base your future calculations on the fact that your target is greater or smaller than 1500.
E.g. if the key is 1650, multiply by 3 to get 4950, divide by 2 to get 2475, subtract your target from 2475 to get 825, which is half of your target.
Or just subtract 1 divide by 2, to name a few methods.
X=115792089237316195423570985008687907852837564279074904382605163141518161494337
Y=115792089237316195423570985008687907852837564279074904382605163141518161494336
If X represents a zero in the calculations of your library, a good mathematician would logically use Y and add 1 to the result.
Like
(Y-pk)+1
So the expert mathematician would use Y and then adds 1? I wonder about the logic in doing that, he might be crazy if he thinks that he can use a different algorithm to find secp256k1 keys faster. Are you sure this "good mathematician" knows about mod n in secp256k1 curve?
Anyways, when searching for unkown keys, doesn't matter if the keys are greater than n or not, because you don't have the pk to check, though if we use standard implementation then we can be sure all keys are valid since they are all calculated mod n, whatever you do, public keys are always mod p, otherwise you get invalid public keys.
When we are talking about bitcoin's curve, you can NOT use different values expecting the results to work on bitcoin keys.