I also would always advise someone to cultivate all four satipatthana, but since you quoted from Perspectives on Satipatthana, I did want to point out that Venerable Analayo, in his first Satipatthana book, states (p. 22):
Several discourses relate the practice of a single satipatthana directly to realization.
The discourses he cites are:
SN47.11
And how, Sāriputta, does one have a liberated mind? Here, Sāriputta, a bhikkhu dwells contemplating the body in the body, ardent, clearly comprehending, mindful, having removed covetousness and displeasure in regard to the world. As he dwells contemplating the body in the body, the mind becomes dispassionate, and by nonclinging it is liberated from the taints.
“He dwells contemplating feelings in feelings … mind in mind … phenomena in phenomena, ardent, clearly comprehending, mindful, having removed covetousness and displeasure in regard to the world. As he dwells contemplating phenomena in phenomena, the mind becomes dispassionate, and by nonclinging it is liberated from the taints.
SN47.37
Bhikkhus, there are these four establishments of mindfulness. What four? Here, bhikkhus, a bhikkhu dwells contemplating the body in the body, ardent, clearly comprehending, mindful, having removed covetousness and displeasure in regard to the world. As he dwells thus contemplating the body in the body, whatever desire he has for the body is abandoned. With the abandoning of desire, the Deathless is realized.
“He dwells contemplating feelings in feelings … … mind in mind … phenomena in phenomena … having removed covetousness and displeasure in regard to the world. As he dwells thus contemplating phenomena in phenomena, whatever desire he has for phenomena is abandoned. With the abandoning of desire, the Deathless is realized.
and SN43.12
And what, bhikkhus, is the path leading to the unconditioned? Here, bhikkhus, a bhikkhu dwells contemplating the body in the body, ardent, clearly comprehending, mindful, having removed covetousness and displeasure in regard to the world: this is called the path leading to the unconditioned….”
x … “And what, bhikkhus, is the path leading to the unconditioned? Here, bhikkhus, a bhikkhu dwells contemplating feelings in feelings, ardent, clearly comprehending, mindful, having removed covetousness and displeasure in regard to the world….”
xi … “And what, bhikkhus, is the path leading to the unconditioned? Here, bhikkhus, a bhikkhu dwells contemplating mind in mind, ardent, clearly comprehending, mindful, having removed covetousness and displeasure in regard to the world….”
xii … “And what, bhikkhus is the path leading to the unconditioned? Here, bhikkhus, a bhikkhu dwells contemplating phenomena in phenomena, ardent, clearly comprehending, mindful, having removed covetousness and displeasure in regard to the world: this is called the path leading to the unconditioned….
I do believe that it is possible to reach liberation through specializing in the practice of one satipatthana, but that’s only because the other satipatthanas, and indeed all other relevant dhammas, will necessarily be experienced and understood before liberation is reached. It seems to me that one cannot contemplate very deeply on any one satipatthana without encountering all of the others, inextricably interwoven as they are.
It seems to me that’s what you’re saying too, sandundhanushka.