Yeah I would assume that kinetic control would predominate in theory. That seems to be the only logic to follow but I have seen that there can be other factors at play that one (I) may not predict until the experiment is done.
So my initial thought on sterics was to protect the tertiary alcohol with something like TBDPS or TIPS, which are larger than TBS, but it may prove difficult. Tertiary alcohols are the hardest to protect but using TBSOTf, 2,6-lutadine, DMAP in DCM should work fine based on the literature. There is also the possibility of using a PMB group, which is a go-to for tertiary alcohols, but may not have the steric bulk I am looking for. The LDA (or HMDS) is also very bulky and should allow for deprotonation specifically under the kinetic conditions.
Do you think with all the factors that it is not unreasonable to think it is possible?