The underlying purpose of tree paste is twofold. Clay as a tissue rejuvenator. Manure as a rich source of microbes. Nutrition is always good ... but that is not especially pertinent here. Anything added like rock dusts may help feed the microbes but don't expect that of bark absorption. I don't even know that the 10% sand portion helps all that much as far as "adhesion" goes. The one other addition I recall others speaking about has been equisetum (horsetail) tea as part of the mix. Silica always has relevance so I get that ... but you would need to be prepared with dry herb from the season before to be able to use this in early spring. That timing is most typical and suits the shifting out of problematic organisms.
Focus now on microbes. Sheep manure should be equally apt as cow. I don't know the critters in either and can offer just one anecdote. A traditional healing method from the Olde World was to apply a "fresh manure poultice" to a badly infected wound overnight. A day later the pus and smell would be gone and new healthy tissue could be seen along the edges of the wound. Manure brought about an organism shift. That's what we want for our trees. Good compost or rich earth probably has what it takes. Effective microbes offer a more limited profile of organisms, and it would be the lactobacilli that would do the most good. Only I don't think near on the level of the ones who thrive in fresh manure.
Others can speak to spraying tree paste slurry. I have only done the "slather with a brush" method. Which I think suits Liz's need as regards black rot canker on larger limbs.
A couple herbal bits as regards shifting canker populations. A blast of fatty acids (fish, neem) can serve to soften the protective lipid coating which organisms use to get through the dormant season to a new spring. This is a core part of the "fatty acid knockdown" strategy to get at bud organisms. Microbes in tree paste applied the next day would find good feeding. Alternatively, some form of chopped garlic (to release the allicin) would flood the canker rim with antimicrobial compounds ... but maybe that's getting too hands on in a commercial block.
These are the sorts of things to think about when contemplating the relevance of biodynamic tree paste.
Lost Nation OrchardZone 4b in New Hampshire