Does the split brain disprove a materialistic mind?
The question title reads:

Does the split brain disprove a materialistic mind?

The simple answer being no, nothing disproves that - the brain harbors the mind e.g., (Lilienfeld &amp; Arkowitz, 2008).
Now you mention that two hypotheses on split-brain patients are false, namely...


Both [hemispheres] gain their own conscious mind.

Only one [hemisphere] has a conscious mind.



...and I agree with them being incorrect hypotheses as suggested in the linked pages.
Now you proceed with...

[Does a] single conscious mind operates across both [hemispheres ?]

Importantly, you state yourself that...

[...] there are [...] other pathways between the hemispheres besides the corpus callosum - such as thalamocortical circuits [...] and those via the midbrain and brainstem [...].

So from my perspective, up until now you have answered your own question whether one single mind operates across two hemispheres in split-brain patients. Anyway, to illustrate some additional interhemispheric commissures besides the callosal pathway, see Fig. 1. This shows that 'split-brains are in fact not entirely split; only the main causeway is severed.
Now there are wild stories about split-brain patients having a dual consciousness, including the paper by Joseph (1998) where the author speculates that one of his patients &quot;...was possessed of two minds&quot; based on the frustrations experienced by this person because his motor skills were erratic. Andrew &amp; Akelaitis (1945) explain that split-brain patients can display diagnostic dyspraxia by an unbalanced inhibitory influence of the dominant hemisphere over the non-dominant side, explaining the uncoordinated behavior on the non-dominant side. These symptoms generally diminish over time, as the brain deploys alternative inter-hemispheric routing of communications.

Fig. 1. Interhemispheric pathways are indicated by numbers 1, 2, 3 and 4. source: Urbanski et al. (2014)
References
- Andrew &amp; Akelaitis (1945) Am J Psychiatr; 101(5): 594-9
- Joseph, J Clin Psychol (1988); 44(5): 770-9
- Lilienfeld &amp; Arkowitz, Sci Am Mind (February 2008)
- Urbanski et al., *Front Integr Neurosci (2014)