Singleton mentions, i.e.~entities mentioned only once in a text, are important to how humans understand discourse from a theoretical perspective. However previous attempts to incorporate their detection in end-to-end neural coreference resolution for English have been hampered by the lack of singleton mention spans in the OntoNotes benchmark. This paper addresses this limitation by combining predicted mentions from existing nested NER systems and features derived from OntoNotes syntax trees. With this approach, we create a near approximation of the OntoNotes dataset with all singleton mentions, achieving ~94% recall on a sample of gold singletons. We then propose a two-step neural mention and coreference resolution system, named SPLICE, and compare its performance to the end-to-end approach in two scenarios: the OntoNotes test set and the out-of-domain (OOD) OntoGUM corpus. Results indicate that reconstructed singleton training yields results comparable to end-to-end systems for OntoNotes, while improving OOD stability (+1.1 avg. F1). We conduct error analysis for mention detection and delve into its impact on coreference clustering, revealing that precision improvements deliver more substantial benefits than increases in recall for resolving coreference chains.