This study uses the concept of dilemmatic space to unpack the complexities of teachers' work when it comes to assessing students in the GenAI age. A key idea of dilemmatic space is that dilemmas are not 'out there' but constructions based on individuals' priorities, knowledge and values. Therefore, studying what teachers perceive as 'dilemmatic' or 'in conflict' is important for understanding how they position themselves as teachers and what they prioritise in assessment when advanced technologies like GenAI become increasingly integrated into our everyday work and lives. Drawing on 636 Reddit posts related to university teachers' experiences with GenAI over a 16-month period, we identified four major dilemmas and 13 pairs of conflicting priorities. Teachers have consistently identified AI-enabled cheating as their key priority to address in assessment but what they specifically saw in tension with this priority varied. Findings shed light on multiple under-discussed issues related to GenAI use in assessment, including teacher autonomy, career security, teacher-student relationship and teacher professional identity. Very few teachers have reported dilemmatic experiences related to their own use of GenAI to assist in their grading and feedback provision, which could reflect teachers' limited awareness of the ethical implications involved in teachers' GenAI use.