/o/ and /u/ in Timucua -- distributional oddities

/o/ and /u/ seem to be different phonemes in Timucua.  At least there are multiple words that differ according to /o/ vs /u/ in some way that is not predictable:

atulu  'arrow'
mucu 'eye'

atichicolo 'heart, soul'
anoco 'lord'

Nevertheless, there is an apparent restriction on the vowels of adjacent syllables within a morpheme, such that /uCu/ and /oCo/ are very common, while /uCo/ and /oCu/ are rare or restricted.

For the /oCu/ combination, we find only instances in Spanish loans or in multimorphemic words:
Comuninoni  'commununion'
descomulgado 'excommunicated'

ano-hubaso-no  'love (honored argument)'

There are orthographic counterexamples for words spelled with , where these represent /kw, bw, fw/, e.g. /ofweno/ 'after', /bweta/ 'for, to'.

For the /uCo/ combination, there are a few common Timucua words:

chumo 'resemble, be like'
calubo 'punish'
hulubo 'farm, till'
nubo 'daughter-in-law'

However, in these examples, the consonant between /u/ and /o/ must be labial.
There are almost no examples of /uCu/ where /C/ is labial.

Thus we seem to have a phonological restriction that in adjacent syllables, non-low back vowels (/u,o/) must agree in height.  And a rule like

/u/ --> /o/ / [C]              ____
                  [+ant, -cor]