How do I configure my package so the stdout and stderr are redirected to a file for the service I'm running?

I'm creating a custom package for a custom service I need to run on my OpenWRT board. I have the following in the /etc/init.d/my_service file:

	# Send stdout/stderr output to the system log
	procd_set_param stderr 1
	procd_set_param stdout 1

With that, I can perfectly see the service output from the syslog live with logread -f. My question is, how can I redirect to a file instead of syslog?

I have tried the following but nothing seems to work:

procd_set_param stderr 1>/var/log/my_service.log
procd_set_param stdout 1>/var/log/my_service.log

That one creates the my_service.log into /var/log but then nothing is written, even if I do chmod a+w /var/log/my_service.log

I also tried:

procd_set_param stderr /var/log/my_service.log
procd_set_param stdout /var/log/my_service.log

And that doesn't work either. It doesn't even create the file.

I have also tried

procd_set_param command $PROG  > /root/my_service.log 2>&1

#procd_set_param stderr 1
#procd_set_param stdout 1

That also doesn't work.

I'm out of ideas. does anyone know how to do this?