task-fMRI to determine TMS site (online stimulation with that same task)? I am planning an experiment whereby rTMS would be administered to subjects while they perform a language task, with the hopes of improving performance on this task as compared to sham stimulation.

Due to the novel nature of this task, it is difficult to predict the most optimal region which to choose as a stimulation site. Someone in our group suggested to run this task in the scanner, and choose as the stimulation site the main cluster that the task activates, in other words the cluster that comes out of the fMRI contrast relevant for this task.

This however seems to me excessively data-driven, as well as somehow circular (though it would not be correct to quite call it double dipping).

Does this approach make sense at all?
This is not a circular question. In fact, using fMRI to create targets is useful to determine TMS targets outside of the motor cortex or visual cortex. See the study here that used fMRI during a task to generate TMS targets, and then applied theta burst stimulation to those targets: https://www.pnas.org/content/113/21/6059

BOLD contrasts are very useful when using TMS to target sites outside of motor cortex, visual cortex and frontal eye field, where TMS can be validated functionally using motor evoked potentials (MEPs), phosphenes or saccadic eye movements, respectively. Brainsight TMS Navigation enables BOLD contrasts (or peak MNI co-ordinates derived from BOLD contrasts) to be entered as targets for TMS.