I find practicing slowly helps a lot. I practice slowly and think about relaxing as much as possible, playing with as little stress as possible. Once I've done that for a week or two. or to the point where it is physically pleasurable to play the piece, speeding up is pretty easy, even speeding up a great deal all at once. I've never found gradually ramping up speed to be helpful.
On point, what I have found, (using Taubman, Mark, and Rachmaninoff together), is that you take a deep breath and then first decide whether or not it is time to put this particular piece aside and come back to it later. If your brain is fried on this piece, all the practice in the world will not work!
Yes! I've had pieces that I've agonized over and eventually learned, but could never reliably play well every time. Then, after putting these pieces aside a while (like a year) and re-learning it, it's like magic. The re-learning is quick, and I'm able to play them infinitely better than I did the first time around. I feel like some pieces really need to marinate in the subconscious for a good long while.