You may have to experiment a bit to get it to set. Do you own an OBD II tool? They aren’t super expensive and are reported to be easy to use. You may just have to repeat that protocol a few times, and keep checking on your own.
I think if I had this problem I’d visit a Toyota dealership shop and ask them what driving pattern is needed for that monitor to complete. They probably deal with this quit a bit, and they are the experts. Visit during a day/time when they aren’t very busy.
It’s also possible the ECM is losing power for some reason, temporarily. That could cause this symptom. The ECM would randomly keep starting over with the monitors. And maybe the cat monitor is just the one that takes the longest to complete. A bad/loose fuse to the ECM, bad battery connections, battery on the fritz that drops out on bumps, etc. Maybe get your charging system and battery tested.
All this sound pretty frustrating. All you want to do is get the car smogged, but no clear way to get past this hurdle. If all else fails, you might try phoning up the Calif BAR and see if they can offer a solution. Or take another look at their website. Unfortunately, if the website is still like it was when I was going through a similar problem about a year ago, the BAR website isn’t very well organized, almost to the point where it appears the BAR is trying to obfuscate the issues and how the owner can resolve them for some reason. But if you phone you may get someone willing to help. If this is the first time this has happened, I think there’s probably a second way to get around all this. But you’d have to fix it by the time the smog test is needed again, in two years.