Let's try this again, shall we? I predict that min sum is 375 and that a winner is me.

This solve was originally titled "Multitasker's Wet Dream". However, the current title is way funnier, especially if it's still wrong. (credit prayformerci)

This is a New Solution 3, made in bed at 4am on a Saturday morning. It was built around arm 1, but arm 3 is the true miracle here.

Despite having invested much less time this week than planned on OM due to illness, I still think I've hit sum gold.