First, find someone with a Hunter GSP9700. GSP9700 Locator
Have them perform a match mount. While you mentioned they reindexed the tire on the wheel, maybe they just reindexed without knowing what the values were, where the peaks were, and whether that was going to fix the problem.
Second, truing a tire may not fix your problem - which is why the procedure kind of died out. Ya' see, only about 60% of a tire's uniformity is tied to runout. The rest is tied to stiffness, which you can't fix.
Third, it might be that the wheel isn't center pikloted - meaning, the wheel isn't being centered on the hub. Are these after market wheels? If so, then you might need a hub ring to get them centered.
And lastly, just because you can't see wobble in the wheel doesn't mean it isn't there. a small amount of wobble at the wheel is amplified at the tire. That's where the Hunter GSP9700 comes in. It also measured the wheel. The key to all this is the operator.
So if you find a GSP9700, have the operator make a note of the before assembly values, the before values of the tire and wheel (2 separate numbers), what the predicted matched value is going to be, and what the final value was. Just be aware that a tire can flatspotted so much that the flatspot is permanent, and can't be corrected by matching the high spot of the tire to the low spot of the wheel.