Just tried Syncthing Lite - it’s brilliant! It let’s me fetch files from home on the off-chance I need them. Really brilliant.
What would make the app perfect for me would be the ability to select a folder to keep a local copy of, and a thumbnail view for a folder that works without having a copy of all of the files inside that folder (I know, I know!).
It’s really very close to something excellent. Thanks @Nutomic