Hire media placement pro with track record. If you want to be in The New York Times, The Wall Street Journal or Harvard Business Review, then the media rep should have placed a number of op-eds there.
This will cost you. The negotiations usually entail other options if that doesn't work. For example, for the original fee, the rep will then try several other brandname publications. If you chose the right media pro, then the op-ed will eventually find a home. Having that media clip will help you get the next op-ed placed in your first or second choice.
Strike while the iron is hot - or better yet, as the issue is heating up. Timing is everything. Your expertise is delivery of services to disabled children. You know that the trial is scheduled for Gigi Jordan. She is the mother who allegedly murdered her autistic son Jude Mirra. You not only prepare your op-ed on an aspect of disabled children. You have your media placement rep shop it around. That rep says you welcome revamping the piece to meet the editor's specific requirements. Your rep will be moving fast.
Be (somewhat) contrarian. Almost half the TED Talks which resonate are contrarian. You might not be a big risk taker. But you don't have to be to take a contrarian stance that is provocative enough to get attention. A little goes a long way. If the meme out there is for the balance of work and personal life, argue there are phases in careers when that's impossible. No, you're not asserting work/life balance is hogwash.
Simplify. That means this: Have your understanding of the subject and the position you're taking down cold. Then you can boil all that to its essence.
You frame that essence in just enough data. No, you don't give 5 examples. You provide only 1. The insight you provide is yours, not platitudes. The tone, word choice, organization, and pacing are conversational.
After the first draft, you go through it again and hunt down any and all complexity.
Have shocking title and first sentence. "Shocking" means non-cliche. In this era when so many media properties play the same story with the same angle, anything that hasn't become a cliche is, well, shocking.
Provide solution. This is a must. No one will put up with your call to a national conversation about the topic. You are expected to put your neck out there and indicate what could be effective.
After the op-ed is published, then you repurpose. That is, you leverage that credential and its content for myriad other kinds of public relations and marketing outreach. For instance, you pitch yourself for a keynote or a panel at your industry's trade association. Do that and more and you will have a significant return on investment (ROI) on the money and time for the original op-ed.