Created a new directory on the shared /nas that all the search heads use
Copied the tsidx file that was the 'most full', as I had done some backfilling manually, to the new directory on the shared storage
Deleted the tsidx directories on the search heads local storage, and replaced with a symlink to the new directory on shared storage
Turned the search heads back on.
This has been running well for a few days, and the tsidx data is being updated by all search heads. Since the search that populates the data is only run by one search head, there have been no collisions so far.