Despite decades of progress in human language technology (HLT) and growing research interest in endangered languages, practical uptake of HLT in documentary linguistics workflows remains rare. In this opinion piece, we report on a structured dialogue among approximately twenty academics convened to diagnose why this gap persists. Across all topics, we identify a recurring structural problem, which we call the missing middle: despite the existence of many potentially useful HLTs, the connective infrastructure necessary to make them genuinely accessible to linguists and language communities does not exist. We report the details of our discussion and make four specific recommendations for how those active in language documentation and HLT research might orient their future work.