Why do delays and rude receivers still wreck my whole run?

You said it yourself: the deliveries you can handle. It's the delays and the hard receivers that throw you off. Notice what that means. The work itself isn't the problem. Your reaction to the normal parts of the work is the problem. Every run has weather, traffic, and at least one person having a bad day. You know this. You've seen it a hundred times. Yet each time it happens, you treat it like an emergency, something that shouldn't be there. That's the mistake. You're surprised by rain in the season of rain. This is not about becoming thick-skinned or pretending delays don't cost you time. It's about where you put the shock. Stop spending it on the fact that trouble showed up. Start spending your energy on how you meet it.