Factors leading to instability as a cluster:
- absence of unmetathesized sequence in language: there are no sequences of [kp] or [gb] attested in the language. Winfield does not include any in his careful treatment.
- the metathesized sequences [pk] and [bg] are very frequent, as the listing below indicates
- the two sounds are similar acoustically

Note that there are no verbs of the relevant conjugation classes ending in dental (non-retroflex) /t/ or /d/.

-ka is a common plural suffix
go@bu, branch of a bush, sg.
go@pka, pl.

-ka is also a suffix added to indefinite numerals 'to indicate the full measure of the article for which the word stands.'
bo@ga, a basket
bo@geka, a basket full

sa@karcci, a span
sa@karcaka, a span's length

First verbal conjugation is generally formed with the addition of the suffix -a (p. 58ff). All verbs end in one of the following consonants: k s t T p h r R l (T, R = retroflex). The author points out on page 72 that an alternate formation in common use uses the suffix -ki.

Third conjugation: these verbs are generally conjugated by adding the suffix -va. For five of the verbs, -ki is suffixed to the verbal base which is first strengthened by the addition of p.
di@va, to fall
di@pki, present verbal participle

giva, to do
gipki
ki@va, to pour
ki@pki
si@va, to give
si@pki
vi@va, to shoot
vi@pki

-ka is also a motion particle inserted between the verbal base and the tense and personal suffixes, p. 112ff. When added to verbs ending in /p/ or /b/, you'd get a [pk, bg] cluster.
ves- veskai
sa@p- sapkai
al- alkai

-k is added to the end of a verbal base to form plural action mode, e.g. one person doing a number of things or one thing many times, more than one person doing a number of things or one thing many times.

When the verb ends in -p or -b, you get the sequence [pk], e.g. se@pa, simple form of verb vs. se@pka, plural action infinitive

Perceptual Optimization: Hume (1998, 2001) argues that consonant/consonant metathesis like that observed in Kui occurs in contexts of low salience and serves to enhance the syntagmatic and paradigmatic contrast of the sounds in that context. The low salience of the sequence stems from the observation that the labial and velar stop are acoustically and auditorily similar. The metathesized sequence of sounds is superior to the expected unmetathesized form in terms of the overall perceptual salience of the segments involved. In Kui, this is achieved by reordering segments in order to improve the salience of a neighbouring sound or sounds; that is, placing the velar consonant in prevocalic position and the labial in postvocalic position. Evidence suggesting that the perceptibility of the segments in this order is greater than in the reverse order comes from an experimental study by Winters (1999). In that study, the salience of consonant place in the context VCCV suggests that positioning a dorsal stop consonant in prevocalic position, even when unstressed as is the case in Kui, provides a greater boost in perceptibility than it does for a labial stop consonant (see Hume 2001 for additional discussion).