You erred, you know that. Everybody does. Honest mistakes may, in my experience, be overcome, but how you respond to them is crucial. I once committed an error that cost my employer, a very sizable international corporation, roughly $400k. While everything was being worked out, I experienced some days of nausea, but thanks to my boss’s wise counsel and assistance, I was able to get through it without losing my reputation. At that organisation, I eventually received a promotion to director.
Even though it’s terrible, if it were me, I would attack this head-on and not offer any justifications.
If it were up to me, I’d choose the best course of action and provide a compelling argument for why it should be taken—which seems like you’ve done already. In addition, I would write it up as clearly as I could in a location that is available across the organisation but difficult to stumble onto and won’t immediately send out a signal to anyone - like a Google doc, Confluence page, or whatever technology is similar in your business.
Before putting together a plan to spread the word, I would first get my manager’s approval on the best course of action. I would then reach out to the leaders of the relevant functions, then down the organisational chart of each other function, to ensure that no one is taken aback when peers reach out to them.
I wouldn’t spread the word about the strategy until you and your leadership have agreed on how to do it. When you are aligned, you could make the document more public afterward.
The document will provide you a consistent message to refer back to in all encounters. I’d decide with my manager who needs a face-to-face/Zoom call, who needs a slack message, who can get by with an email, etc.
I would provide a sincere apologies at each stage and throughout the document. That will consist of three components, in brief:
I apologise.
Absolutely my responsibility
Will not occur again
More on apology in this post on reddit.com
Always acting morally is the right thing to do. If you attempt to ignore it in any way, it will almost certainly backfire and make you appear worse in the eyes of your coworkers. You might actually increase your overall credibility if you take it on head-on, own it, and lead the charge back to the appropriate course for the product and business (for reasons explained in the thread I liked to above).
Of course, it’s up to you; you are the expert on the issue. However, I’ve had nothing but success using this strategy.
Good luck, my friend!