One thing that someone showed me with rendering hard to get scenes is set the max samples to -1. That basically makes it so that there is no cap, it will run until it hits your % threshold. Be it 500 or 25,000 or whatever max time you set.
Thank you for the advice! However, I've already tried that kind of thing and it didn't work for me.
Also, I don't work with Convergence anymore. I have found Convergence to be, more often than not, an unreliable parameter that has no real grip on quality. Your render can be 100 % converged and still noisy, especially if you render at lower render quality (which only effect, by the way, is to multiply your iterations).