That rules out DHCP lease renewal as a cause for the rewrite.
I'm out of ideas as to what's causing this...
As another attempt ot preserve a public DNS server during installation, you could try altering resolvconf's default settings:
sudo nano /etc/resolvconf/resolv.conf.d/head
# Dynamic resolv.conf(5) file for glibc resolver(3) generated by resolvconf(8)
# DO NOT EDIT THIS FILE BY HAND -- YOUR CHANGES WILL BE OVERWRITTEN
nameserver 8.8.8.8
Exit with saving, then restart resolvconf:
sudo systemctl restart resolvconf.service
Check contents of resolv.conf to verify this worked:
cat /etc/resolv.conf
To be sure, reboot your Pi-hole machine and double check.
If your public DNS server is still present in resolv.conf, you're ready to retry Pi-hole's installation script again.
EDIT:
Don't forget to remove your public DNS server from /etc/resolvconf/resolv.conf.d/head once you're done.