For each service, create a rsyslog configuration in /etc/rsyslog.d/FILE.conf and give it 644 permissions:
if $programname == 'PROGRAM_ID' then /path/to/log/file.log
& stop
For multiple services starting with same name:
if $programname startswith 'PROGRAM_ID' then /path/to/log/file.log
& stop
In the service file itself, add:
StandardOutput=syslog
StandardError=syslog
SyslogIdentifier=PROGRAM_ID
Finally, run sudo systemctl restart rsyslog.