A cover letter that doesn't sound like everyone else's

Here's a job ad:

Operations Coordinator, mid-size logistics firm. You'll own scheduling for a 40-strong driver pool, keep our routing software up to date, and be the first point of contact when something goes wrong on the road. We're looking for someone calm, organised and comfortable saying no. Experience with TMS software preferred.

Here's what I've actually done:

Four years running the front desk and rotas at a busy vets, 18 staff, I built the on-call rota everyone still uses. Before that two years in a call centre doing complaints. No logistics software but I taught myself the vets' booking system and trained everyone else on it.

Why I want it: I'm good at the bit where everything is on fire and someone has to stay calm, and I want to do that somewhere with more scope than a vets. It's also ten minutes from my house.

Write me a cover letter. Under 250 words, four short paragraphs, no bullet points.

Rules:
- Every claim has to point at something specific from what I told you. If you can't back a sentence with something I said, cut the sentence.
- Use my words for what I do. Don't feed the ad's phrases back at them.
- No "I am excited to apply", no "I believe I would be a great fit", no listing adjectives about myself.
- Open with the thing about me that's most relevant to this job, not with the job title.

Then, separately from the letter, give me two lists:
1. What the ad asks for that I can't evidence from what I've told you. Don't write around these gaps in the letter, just tell me they're there.
2. Anything in my background that I've undersold and should have led with.

What you get: A short letter with no filler, plus a straight list of the gaps in your application.