As to how to apply this to formal practice, I'm not one hundred percent sure. First off, there are parts of the Tefillah that if you don't have proper kavannah, it's as if you didn't pray at all. (most important among those: the first two passukim of Shema Yisrael, and the first blessing of the Amidah (aka. the shemoneh esrei)) If in such a situation, you didn't have kavannah, I would imagine you should go back and repeat those parts. I'm not a Rav, so consult your Rav to find out exactly.
If you still would like to heed the Holy Zidichover Rebbe's words, then perhaps there's something we can do. When you do (for reasons of lack of kavannah) go back over any part of the Tefillah that you are halachically permitted to repeat, then have in mind that you aren't erasing the previous thoughts, but rather infusing them with additional life and returning them to their soul roots. [The Baal HaTanya brings down that Tefilloth said without kavannah stay down in this world until they hitch a ride on a later Tefillah said with appropriate kavannah. So as I said above, it seems to me that your intention should be to provide the earlier prayers with a ride to hitch on to. In that way, we can satisfy Halachah as well as the words of the Holy Zidichover and the Holy Baal HaTanya. But of course, in matters like this, consult your personal Rav/Rebbe.]