To me finesse fishing stained water is more about the color lure you present than anything else. I steer towards the black, black/blue and junebugs when presenting finesse lures in stained water.
A few examples is a T-Rig Senko, a black finesse worm on a shakey head, black/blue jig and baby rage trailer or a beaver style bait.
Seems to do well for me in those situations.
One fun technique that I have tried a little bit with some success is an MJ rig with a small gold colorado blade. It worked decently when I fun fished a few times. I didn't have the confidence to try it during tournaments yet. If you give this one a shot let me know how it worked out.