First of all, you will need to disable DHCP on your router (or change it to give out your new DNS server addresses), having two on a network is not a good thing.
Second you will need to renew DHCP lease on every device, because devices will not do it automatically until their lease expires.
You've mentioned you can't turn DHCP off on your Actiontec T1200H, but to quote the manual:
"To change the Gateway's DHCP settings: 1. Click Enable to activate the Gateway's DHCP server."
Now what some telecommunications companies do is they give you a username and password that is limited to setting up WiFi, rebooting and doing some other basic settings. What they don't tell you about is there is another set of credentials to allow full control over the router. You don't get these because you can screw it up and they have to come to your house to fix it.
Try calling your ISP and asking for this administrative user/password (good luck with that) and try Google searching your specific ISP/gateway combination for administrative password, someone probably figured it out.
__EDIT
PPoE settings are for VPN, and DHCP can assign IPs to VPN clients, but it's not DHCP itself.
Here is an example of what I mean:
I use Telekom Srbija as ISP and they gave me a username "user" and password "123456" to log into my gateway. This user can't change DHCP settings. 
So I went online and typed into Google search "Telekom Srbija ADSL admin user" and it came up with username "admin" and password "adminpassword". Logging in with these gave a much different menu and access to changing DHCP. 