Vähän kohtelias
A bit polite. You are reading most of it right and still padding the edges - an extra softener here, a second apology there.
The fix is to cut rather than add. Kiitos at the end of a request does the whole job, anteeks once is enough, and a bare ei tartte is friendly exactly as it stands.
From How Rude Is Your Finnish? - 6 lines of real spoken Finnish on Finnish IRL.