End-to-end relation extraction (E2ERE) is an important task in information extraction, more so for biomedicine as scientific literature continues to grow exponentially. E2ERE typically involves identifying entities (or named entity recognition (NER)) and associated relations, while most RE tasks simply assume that the entities are provided upfront and end up performing relation classification. E2ERE is inherently more difficult than RE alone given the potential snowball effect of errors from NER leading to more errors in RE. A complex dataset in biomedical E2ERE is the ChemProt dataset (BioCreative VI, 2017) that identifies relations between chemical compounds and genes/proteins in scientific literature. ChemProt is included in all recent biomedical natural language processing benchmarks including BLUE, BLURB, and BigBio. However, its treatment in these benchmarks and in other separate efforts is typically not end-to-end, with few exceptions. In this effort, we employ a span-based pipeline approach to produce a new state-of-the-art E2ERE performance on the ChemProt dataset, resulting in $> 4\%$ improvement in F1-score over the prior best effort. Our results indicate that a straightforward fine-grained tokenization scheme helps span-based approaches excel in E2ERE, especially with regards to handling complex named entities. Our error analysis also identifies a few key failure modes in E2ERE for ChemProt.