Ya know, Lincoln's toe-tapping may be less physical and more psychological than is typical...He has had so many different diets, and each time you change them the toe-tapping stops, then eventually, within a certain amount of time (whatever that usually is), the toe-tapping returns, until you once again change-up his diet, then it goes away again for a while, etc. So it may very well be that Lincoln is simply getting bored with his regular, daily diet after a certain amount of time, and whenever it is that that happens, his toe-tapping returns, but not as a symptom of a physical or metabolic issue, but rather an anxiety issue. So just putting him on an always-fluctuating or rotating diet that you simply automatically change BEFORE THE TOE-TAPPING STARTS AGAIN may just be the answer...
For example, if Lincoln usually starts toe-tapping again around 2 months after you first change-up his diet (I'm just picking a time period at random, use whatever the average amount of time is between the changing of his diet and then the restart of his toe-tapping), then instead of waiting for the toe-tapping to start again, from now on just automatically change-up his diet again after a month and a half, BEFORE he starts toe-tapping again, and then see if it still returns...If you do this and the toe-tapping doesn't come back, then again just automatically change-up his diet at a month the next time, and so on. It's very likely that if Lincoln's toe-tapping is actually a psychosomatic anxiety response to boredom or to his regular, daily diet, for whatever reason, then that means that he may have just gotten stuck in a routine of automatically starting the toe-tapping to get you to change up his diet! It's not far-fetched, it's just like the "If I scream they come to me, so I'm going to scream" thing. Lincoln could very well be going "When I toe-tap she changes my food, so I'm going to toe-tap". Or it could be less of a conscious decision for him than that, he may just unwittingly do it as an autonomic response to boredom with his food. Either way, you have to break the cycle, and the way you do this is by changing up his diet BEFORE he starts toe-tapping again, and do this each month, or each two months, whatever the time period is. Try to anticipate it and change it before he ever has a chance to start. And if you do this for a long enough period of time, it may just break the cycle and stop it.
****And if you think that you have "failed" Lincoln because he toe-taps once in a while due to food boredom, can you imagine what kind of shape he'd be in right now if ANYONE ELSE had him? As finicky and sensitive as Ekkies are to everything, and as many Ekkies that I've seen who are pluckers, who self-mutilate badly, who are an anxious wreck, who cannot be interacted with at all, etc., you've done just a fantastic job with Lincoln...he loves you, and he needs you! And he knows it too!