You've all persuaded me to skip Brno & spend more time in Cesky Krumlov, which leads to a follow-up question. It appears that the best way (weighing factors of expense & convenience) is to take a train from Budapest to Linz -- no changes required -- and then one of the various shuttle services to CK. (Recommendations on the latter welcome. It looks like CK Shuttle/Bean has the best options & most regular service.)
Am I missing anything obvious?