My phone is too janky for LineageOS.

Got the same prolem, S5 'Neo' isn't supported and the unoffial Linage ROMs for it seem to have bad connection.

I have heard that location reporting is a core OS feature, as part of the Play store

I believe it's Play services, but you can delete the playstore andplay services and then use Yalp instead of the play store while blacklisting the downgraded playstore (so it won't update again and install play services).

Some apps will complain that play services is missing but usually will work fine anyhow (Just set their 'messages' to off, so it doesn't up up everyday). {You can use Google maps, it will complain on startup about the 'play services' missing [Probably because that is the ALWAYS ON connection to google] }

You can do this without rooting and without using the system-app remover. Just disable the 'apps' (like play store/services) by deleting them, stopping them and blacklisting them in Yalp so Yalp doesn't download 'updates' for them.

• Disclaimer: I'm not sure about newer phone provided with newer preinstalled playstores (removing it makes it revert to the ROM's default version, so maybe newer phone it gets more dificult.