I would not invest the slightest trust in the catholic church's estimation of value.
I thought, from the title of the thread, that we were talking about what english speaking zen practitioners also refer to as "sitting", which I understand to be a formal training method that is more or less universally practiced by Buddhists.
If fancy pants famous characters want to call other types of practice meditation too, that is certainly their prerogative, but I suspect such overloading of the term is the root of the lack of common ground on the subject.
I guess that having diverse interpretations of esoteric terminology is very apropos to this venue.
When I was introduced to formal sitting meditation in a Buddhist setting, the morning meditation was two periods of seated meditation, joined by a shorter period of mindful walking meditation. There was really no question of this being two periods of "meditation" separated by an "intermission" of movement; what was being practiced was one long period of meditation which passed through distinct modes of practice (Preliminary practices-sitting-walking-sitting-concluding practices).
Even within that framework, there are many possible variations. For example, Mary Malmros referred earlier in the thread to shamatha vipassana, referencing two distinct modes of meditation that are emphasized to various degrees in different traditions. Each of these modes has a long tradition of practice, instructions for practice, and advanced instructions for practice. And each tradition has its own sequence in which it introduces these distinct modes, and relative emphasis on one, the other, or both in some intertwined or sequenced fashion. At no point in thirty years of aikido training have I encountered instructions with anything like the specificity of those for either seated or moving meditation which I first encountered in the Soto Zen tradition.
Moreover, these are not the only modes of meditation practiced within the broader Buddhist tradition-- there are more than a few others. Many of these may look entirely the same to an outside observer, but be entirely different as to the methods and goal of the practitioner. Looking is not seeing, in such a case.
Notwithstanding the DIY bent of much of our culture, if you have specific goals for meditation practice, it's a good idea to a) find someone who has achieved those goals through meditation practice, b) successfully helped someone else achieve those goals through meditation practice and c) get yourself some individual guidance.
Maybe you're entirely right and meditative movement is entirely wrong for you. But that doesn't mean that there's no such thing as moving meditation, or that it doesn't benefit some people.
It just means that the moving meditation which you've encountered doesn't suit your current desires.
For my part, my sense is that the common characterization of aikido as "moving meditation" is little more than a tattered banner on the dusty and largely abandoned fairgrounds that once held the sprawling Carnival of the New Age, a lost phenomenon that now exists in little more than a few remnant populations in Ithaca, Amherst, Boulder, Santa Cruz, and points beyond. And just as Sugano Sensei once responded to a request for weapons training by telling the student "If you want mochi, go to the mochi maker," I think that people who are looking for meditation practice would do well to go to someone with some sound experience in meditation practice, whether Buddhist or Shinto in derivation.
And I would further suggest that, for best results, those from whom you are taking advice about meditation be people whose meditation practice and instruction is in no way dependent on their relationship with any martial arts instructor, particularly as students.
My .02. Hope it helps.