Late detection of emerging viral transmission allows outbreaks to spread uncontrolled, the devastating consequences of which are exemplified by recent epidemics of Ebola virus disease. Especially challenging in places with sparse healthcare, limited diagnostic capacity, and public health infrastructure, syndromes with overlapping febrile presentations easily evade early detection. There is a clear need for evidence-based and context-dependent tools to make syndromic surveillance more efficient. Using published data on symptom presentation and incidence of 21 febrile syndromes, we develop a novel algorithm for aetiological identification of case clusters and demonstrate its ability to identify outbreaks of dengue, malaria, typhoid fever, and meningococcal disease based on clinical data from past outbreaks. We then apply the same algorithm to simulated outbreaks to systematically estimate the syndromic detectability of outbreaks of all 21 syndromes. We show that while most rare haemorrhagic fevers are clinically distinct from most endemic fevers in sub-Saharan Africa, VHF detectability is limited even under conditions of perfect syndromic surveillance. Furthermore, even large clusters (20+ cases) of filoviral diseases cannot be routinely distinguished by the clinical criteria present in their case definitions alone; we show that simple syndromic case definitions are insensitive to rare fevers across most of the region. We map the estimated detectability of Ebola virus disease across sub-Saharan Africa, based on geospatially mapped estimates of malaria, dengue, and other fevers with overlapping syndromes. We demonstrate "hidden hotspots" where Ebola virus is likely to spill over from wildlife and also transmit undetected for many cases. Such places may represent both the locations of past unobserved outbreaks and potential future origins for larger epidemics. Finally, we consider the implications of these results for improved locally relevant syndromic surveillance and the consequences of syndemics and under-resourced health infrastructure for infectious disease emergence.