This paper presents NAVER LABS Europe's systems for Tamasheq-French and Quechua-Spanish speech translation in the IWSLT 2023 Low-Resource track. Our work attempts to maximize translation quality in low-resource settings using multilingual parameter-efficient solutions that leverage strong pre-trained models. Our primary submission for Tamasheq outperforms the previous state of the art by 7.5 BLEU points on the IWSLT 2022 test set, and achieves 23.6 BLEU on this year's test set, outperforming the second best participant by 7.7 points. For Quechua, we also rank first and achieve 17.7 BLEU, despite having only two hours of translation data. Finally, we show that our proposed multilingual architecture is also competitive for high-resource languages, outperforming the best unconstrained submission to the IWSLT 2021 Multilingual track, despite using much less training data and compute.