Contextual biasing enables speech recognizers to transcribe important phrases in the speaker's context, such as contact names, even if they are rare in, or absent from, the training data. Attention-based biasing is a leading approach which allows for full end-to-end cotraining of the recognizer and biasing system and requires no separate inference-time components. Such biasers typically consist of a context encoder; followed by a context filter which narrows down the context to apply, improving per-step inference time; and, finally, context application via cross attention. Though much work has gone into optimizing per-frame performance, the context encoder is at least as important: recognition cannot begin before context encoding ends. Here, we show the lightweight phrase selection pass can be moved before context encoding, resulting in a speedup of up to 16.1 times and enabling biasing to scale to 20K phrases with a maximum pre-decoding delay under 33ms. With the addition of phrase- and wordpiece-level cross-entropy losses, our technique also achieves up to a 37.5% relative WER reduction over the baseline without the losses and lightweight phrase selection pass.