Pardon my ignorance if I am misinformed, but these tulkus are not believed to be “truly” independent beings, but rather, emanations of bodhisattvas of avaivartika [non-retrograding] bhūmis, such as Avalokiteśvara, who emanates the manifestation of the Dalai Lama tulku. Avalokiteśvara does not perish every time that the Dalai Lama perishes, according to the internal worldview of Mahāyāna Buddhism, as best as I understand it, so the issue of how the Dalai Lama is able to “apparently” reincarnate several times similarly is somewhat sidestepped by this postulation of avaivartika bhūmis, coupled with the belief in the supernatural long lives of celestial bodhisattva like Avalokiteśvara.
It seems that it is an issue of differing Buddhavacana that is fundamental here, as this discourse is largely absent from non-Mahāyāna Buddhism, even absent from schools who believed the Buddha was some sort of quasi-eternal Dharma protector (my phrasing). This absence is something that hampers the ability of schools that have this extra layer of teachings to communicate with the older tradition, which lacks it. Concepts cannot be explained because the content of the Buddhadharma is simply larger, more seems to have to be taken on faith (when will I even be able to verify an avaivartika bhūmi?).
I am not trying to speak negatively of any tradition, I am just saying something about the lack of ability to communicate between the schools, in some cases, due to them having different “basic assumptions” about what the Buddha taught.
