Memory-augmentation is a powerful approach for efficiently incorporating external information into language models, but leads to reduced performance relative to retrieving text. Recent work introduced LUMEN, a memory-retrieval hybrid that partially pre-computes memory and updates memory representations on the fly with a smaller live encoder. We propose GLIMMER, which improves on this approach through 1) exploiting free access to the powerful memory representations by applying a shallow reranker on top of memory to drastically improve retrieval quality at low cost, and 2) incorporating multi-task training to learn a general and higher quality memory and live encoder. GLIMMER achieves strong gains in performance at faster speeds compared to LUMEN and FiD on the KILT benchmark of knowledge-intensive tasks.