There are several tools you can use to find out about load. Many frequent fliers will choose their flight not based on convenient times, but on likelihood of getting an upgrade, for example.
- KVS is user-supported and has a really horrible web site, but many people swear by it. You download an app that you run on your machine and it can find routings and show you availability.
- Expert Flyer has a free trial that might be all you need on this trip.
I have never used either, but on the Flyertalk forums, people used to always paste KVS results and these days they seem to mostly post expert flyer results when they're helping each other plan something epic. There could easily be more tools, these are just two I have heard of. There is a big list at http://flyaow.com/classavailability.htm which is a site I used to use to check availability, but which doesn't offer that any more.
Back when I had status, my dream flight was super full in economy (no more seats for sale, or less than 9 in the top few buckets, 0 in the lower buckets, meaning it's overbooked) and wide open in business. That is a flight where op-ups will be happening if all the economy people show up. And yes, I have chosen flights based on that (or chosen for another reason but then monitored my flight), seen that pattern, and got an op-up. But that was long ago.