The situation in Chori exemplifies a widespread problem with discussions of allophony, that "allophone" has different meanings. The classic definition of allophone is that two phonemes (or, tonemes) are allophones iff the variants appear in surface-complementary environments. This is not the case in Chori: all 6 tones are surface-contrastive. The alternative definition is "you could remove some of the tones from underlying forms by applying some set of rules". The data-source, Dihoff, pursues a toneme-minimizing analysis where 1→3/_6, 4→2/_1 and 2→5/_6. The particular rules are well-enough motivated since they apply in phrasal contexts, but the underlying representations are not always motivated. Dihoff notes that these rules may be limited to certain grammatical constructions, for example in the present tense, /1/ becomes  after a 3s subject and /4,6/ become  after a 1s subject. This analysis may be technically tenable if you decompose any  into an abstract sequence /1+6/, but this is entirely contrary to the spirit of the traditional concept "allophone" which is based on distribution in surface forms, not underlying forms. Dihoff's analysis only assumes that you can remove tones /2,3,5/ from lexical entries, it does not assume that you can remove those tones from derived representations, including the surface form. In fact, his discussion starts with a tone-minimizing analysis with just /1,4,6/ but morphs into a full 6-level analysis once he gets to talking about tense-inflection and the like.
IPA allows concatenation of level markers, using either accents or bar-markers, so that contours are irrelevant – you can have rising, falling, high-rising and so on as contours. The only thing that would pose a problem for IPA is a 6th level. As it happens, IPA sort of failed in its remit to specify standard letter-shapes for contours. Given 5 levels, there are very many contour tones than can be created (and that are attested) such as extra-high-to-extra-low vs. extra-high-to-mid vs high-to-extra low etc. But they only provide 5 letters for tone contours, and they leave it to the author to come up with a clever way to indicate more subtle contours. This means that authors dealing with language that have many levels and many contours formed from those levels have to operate outside the IPA system, and use one of the two (mutually incompatible) non-IPA numeric-superscript notational systems.