I typed up below but maybe first try @Bucking_Horn method with resolvconf.
Lets see if we can get it running anyway.
nameserver hack first:
sudo tee /etc/resolv.conf <<< $'nameserver 8.8.8.8'
Get the binary (correct one this time 
):
sudo wget https://github.com/pi-hole/FTL/releases/download/v4.3.1/pihole-FTL-arm-linux-gnueabi -O /usr/bin/pihole-FTL
sudo chmod +x /usr/bin/pihole-FTL
Get the init.d script that should start the pihole-FTL binary as a systemd service:
sudo curl -s https://raw.githubusercontent.com/pi-hole/pi-hole/master/advanced/Templates/pihole-FTL.service -o /etc/init.d/pihole-FTL
sudo chmod +x /etc/init.d/pihole-FTL
Make sure the pihole user exists:
sudo useradd -d /home/pihole -s /usr/sbin/nologin pihole
Create temporary basic config file to supply upstream DNS server:
sudo tee /etc/dnsmasq.conf <<< $'server=8.8.8.8'
Start here up:
sudo bash -x /etc/init.d/pihole-FTL restart
Check if its resolving Github:
host github.com localhost
Run the install script to get rest of the files:
curl -sSL https://install.pi-hole.net | sudo bash -x
If install script fails at some point, try run repair (might need nameserver hack):
pihole -r
Stop pihole-FTL:
sudo bash -x /etc/init.d/pihole-FTL stop
Default below file again:
sudo tee /etc/dnsmasq.conf <<< $'conf-dir=/etc/dnsmasq.d'
Start here up using systemd:
sudo service pihole-FTL restart
And test:
pihole status
sudo service pihole-FTL status
host pi.hole localhost
host github.com localhost
Reboot:
sudo reboot
EDIT: Noticed mistake
EDIT2: I forgot the pihole user
EDIT3: Forgot dependency of config file
EDIT4: Thinking ... it would be easier to just install dnsmasq and disable dnsmasq after Pi-hole is installed 
Added advantage, you get the dnsmasq man pages installed as well