I'm curious how you would go about determining the frequency of your tinnitus.
When you play two square waves that are slightly off, you also hear a really obvious pulse that corresponds to how off they are (1 pulse per second means they're off by exactly 1 hz, and so on.) I don't know what the experience of tinnitus would be, but assuming you can hear the tinnitus and a square wave at a close pitch, it should be fairly easy to isolate the exact frequency with a binary search.
I found a frequency that was pretty close to what I hear (it's convenient that my left ear is mostly normal), and cranked it in my right ear. I now hear something like a distant swarm of bees, or a server room full of very loud fans.