*UPDATE*
I heard back from Blizzard and the ban on my account still stands. After the initial ban wave a few months ago, I delete HB completely off my computer including any remaining folders or registries. I never botted on my new account, however it was on the same battle.net account as the other banned accounts I had. Apparently my new account was banned by association. I have never used any other bots besides HB.
I guess, you have to contact senior game masters to handle your issue.
Unless they are too brainwashed, something I really doubt, they have to act properly.
Btw, the ban for association is usually placed for accounts, indirectly related to gold-trading. Already had one Scarab Lord account banned for this reason in the past. But I guess, they had "hard evidences", since I have sold quite a few gold recently back then, so it was mission impossible to recover it.
The sad part was, that their manual investigation was triggered by player reports, stacked on another 3x licenses, reckless farming Uldum / Twilight Highlands with GB2, back in Cata - all 3x within the same battle.net account. And 2 of these 3 reckless accounts are still up, 4 years later. 1 is active, other is on 6m suspension since 13.5.
So the whole battle.net ban by association to something is really not likely in your case.
Unless you were gold-trading, your ban should be 99% false-positive.