Has anyone ever seen a tool that tries only a set of keys? Let me explain, imagine you have this key
0x397f5aa7b90de4
What if you want to set the public key of this one 0x5aa7b90de4 and then try all combinations for the first 4 missing characters? as I understand it, no tool exist to scan selected parts of a range, or do they exist?
You would have to give a better example of how many leading characters, because what you have now would only take a few seconds/minute, to iterate all possible combos, even with a single thread python script. Even if you do not know the leading character, you are looking at 16^4 combos, 65,536 possible combos.
But initially, I was thinking the same thing as albert0bsd was, it is similar to BSGS, because BSGS basically cuts off the last x characters, depending on your baby step file (how many public keys it contains), but for your specific example, you would need a baby step file with 2^40 keys, or modify the keys known down, to use a smaller size file.
But as is, without mod, you would merely start with 0x1000 + 0x5aa7b90de4; and increment 0x1000 by +=1 until match is found. 0x1000, 0x1001, 0x1002, etc. Not a very difficult script to put together, using python.