Saw you were an intern on the Hill and were asking about DC Congressional on multiple Forums. In the old days, you could get a nom from any Rep who liked you, irregardless of where you lived. It doesn't work that way now. Unused noms from a district go back to the Super. My dad gave his DC nom to his best friend who didn't have one. He took the SODV merit exam for his. It doesn't work that way anymore.
DC is not a terribly competitive district, but you have to be a resident (as opposed to a resider). A Resident is an 18 year old who is self supporting, (or a court emancipated minor) and provides more than half their own financial support.
Unless you are financially independent, you are a resident of where your folks file tax returns, and that is where you have to seek you nom.
Having successfully been through the process 'virtually' as a son, father, and son in law, my takeaway is if an Academy is in your heart, you will find a way.
With respect to noms, Congress and the Services fight some, but they are on the same team, and they do work together. Its tough to get a nom if an Academy signals 'we wont take A, but we like B'. Neither jam each other, they are independent thinkers, but an Academy jammed with a kid they don't want, will find a way to reject him. And a MOC doesn't want to waste noms.
They don't conspire, but they certainly work together to meet the needs of the other.
The answer is, you need BOTH. The support of of your MOC, and the support of Admissions. Then they will work it out.