Ohio RITA local taxes

For 2021, we failed to file a Form 37 with RITA - totally our fault, no excuses. They filed for us based on our W-2s, sent a bill, which we paid.

 

The challenge is this: the reason we hadn't paid is because my husband is an idiot and when he started working from home, he never updated his work location and they continued withholding for his work city instead of our residence city. Both cities have a tax rate of 2.25%, with a 50% credit rate. So, anything withheld for the wrong city only contributed halfway towards our residence city, hence the bill. If the beloved idiot had corrected his work location, we'd have ended up perfect without owing anything.

 

So, I'm making him have work sign a 10A to certify that he lived/worked in our residence city the whole year. However, I'm not sure if that's the right approach because I'm not looking for 100% of the incorrect work location to be refunded because it was already used as a credit towards our residence city. What I really need is those wages/withholdings moved from the wrong city to the right one, then a refund of just the extra we paid that we wouldn't have owed if we'd gotten 100% credit in our lived city in the first place. 

 

Do I file an amended Form 37 with an accompanying 10A? Do I file just the 10A and let them figure out the whole 50% credit complexity? Do I go into my local RITA office and throw myself at their mercy?