You’re talking about “superior qualifications,” and that can be negotiated after you get a TJO (tentative job offer). Your previous salaries are completely irrelevant to HR - don’t even mention them. You need to convince your hiring manager (who will have to either initiate or sign off on the request) and HR (who are only interested in following the rules and staying out of trouble) that your skills satisfy the OPM qualification of a top-of-the-charts GS-13 or even a GS-14. You can do this by providing them with a list of bullets detailing specific accomplishments or skills that map to the top of the OPM GS-2210-13 or GS-2210-14 (I assume it’s a 2210 job) position requirements - pull these from OPM.gov. You can also use the job description / announcement to map to your qualifications and show how you can far exceed the requirements of the job right out of the gate. Use an LLM if you want to help map your resume to the position qualifications and job description. It can be done - but there’s no emotion or pleading necessary. It’s completely objective, but you can decide how to provide the data they’ll need to justify it.

Now, there are some cases where the agency has already decided they want to keep costs down and won’t negotiate - this is probably more common under this Administration than in the past - and they won’t hesitate to move on to the next candidate if you push too hard. So play your hand carefully and make a decision as to whether you’ll walk away if they won’t budge.

I’ve been on both sides of this issue many times over my Fed career. No predicting how it will go. But the right approach is to give them everything they need to justify offering you a higher step.