But if an attacker is unaware of which digit was changed or how many digits changed there is no way to deduce that from seeing the public address. Is there? Maybe I should send some BTC to the address to see if someone will crack it.
That is true, but he is simply going to try all 1 mutation variations, then 2, ... then 3 ... up to whatever budget he's allocated for the attack.
No need to create a bounty ... the corrected version of your private key is:
6108
F178B39FF904C9F408741935554E042BDE257DB7F5621555175BACAC2A9C