To what extent is the popular picture of Sparta in Greek literature (military system/agriculture/diet/living arrangements) either backed up or refuted by archaeology? Are there any one-volume books about this that focus more on fieldwork and less on texts?
There is no one-volume archaeology-focused book on this topic. The studies are much more targeted (for instance, on the excavations at the sanctuary of Artemis Orthia in Lakonia). Also, historians tend to utilize texts to further archaeological understanding, and vice versa.
Having said that: there are some excellent volumes on Sparta/Lakonia which present comprehensive overviews.
Paul Cartledge, Sparta and Lakonia: a regional history 1300-363 Second Edition (Routledge 2002). An excellent comprehensive volume. It weaves all the available evidence (as of 2002) together, including a comprehensive view of Lakonia's various archaeological sites. There is also an appendix specifically on Artemis Orthia.
The "Companion" book for Sparta, which is a sprawling 2-volume set. The goofy name of this series is really unfortunate, because many people assume it is a kid book, or a "for dummies" series. It is not. The Companion books are excellent. This one is now the go-to book for Sparta and Lakonia, with very up-to-date entries for a huge variety of topics: Anton Powell, ed., A Companion to Sparta 2 vols (Wiley-Blackwell 2018). In particular for you: Cavanagh, "An Archaeology of Ancient Sparta with Reference to Laconia and Messenia."