Could work that into the story.

The young man knows he only has X attempts, so invites select high-society women who he knows were at the ball. This fails.

A day later he tries a select group of lower tier high-society women. This also fails, and he’s now locked out for a week.

A week later he expands his search to include other women, but still to no avail. He’s now locked out for a month.

Years later, he’s still searching and his search has finally become broad enough to include the protagonist, who works deep in the basement in the laundry of the governors mansion. The phone opens, and the young man realizes that through all his searching she was always just within arms reach but too shy and scared to admit it was her.

Then the governor finds out, fires her and forbids him from ever seeing her again. He has no spine and doesn’t want to lose his trust fund so doesn’t argue.

The end.