Technically, the Internet Connectivity Check on LineageOS also sends your position/IP to Google, and also avoids a VPN tunnel because it's lower down the stack.
I can recommend LineageOS, however be aware that lots of malware infected builds have made it to xda dev in the past, so you should build it yourself if possible (or use the official downloads).
Regarding the Connectivity Check: You can add all google related domains to /system/etc/hosts if you have root/sudo access.
Additionally I'd recommend everyone to use RethinkDNS as a DNS adblocker and app firewall - and AppWarden to patch out the Analytics parts of proprietary Apps.
I can recommend LineageOS, however be aware that lots of malware infected builds have made it to xda dev in the past, so you should build it yourself if possible (or use the official downloads).
Regarding the Connectivity Check: You can add all google related domains to /system/etc/hosts if you have root/sudo access.
Additionally I'd recommend everyone to use RethinkDNS as a DNS adblocker and app firewall - and AppWarden to patch out the Analytics parts of proprietary Apps.