—“What’s the relationship between truth-telling and dueling? Is it because you should only say something you believe to the extent that you’re willing to fight for it?”—
It’s actually two different issues.
You impose a cost on someone else’s reputation at the peril of your life. Especially after guns were invented. They are a great equaliser.
If you speak truthfully and it imposes a restitution then that is a moral obligation to your fellow citizens.
If you speak the truth in general then that is a cost to you but it is the cost of entry into the informational commons just as respect for property is a cost you must bear for entry into the market.
The purpose of judicial combat was to create time to cool off and apologize, and negotiate a settlement rather than put noble families in feud.
The duel degenerated into sanctioned murder. The problem is preventing duel by construction (murder).
That requires a third party to judge the restitution for the insult.