Do I have to round a limit mark at the finish before I've finished?

No — under Rule 28.1 and the definition Sail the Course, you finish the instant any part of your boat crosses the finish line. A limit mark sitting on the far side of the line doesn't begin, bound or end your last leg, so it has no required side — leave it either side. (World Sailing Case 58.)

▶ Watch on YouTube ↓ Download (via YouTube)
<iframe width="560" height="315" src="https://www.youtube.com/embed/D-2G0XDud5Q" title="Sailing Kiwi" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
<p><a href="https://sailing.kiwi.nz/v/D-2G0XDud5Q/">Source: Sailing Kiwi</a></p>