If I am reading your description correctly, you have two services from your SP that each drop off a vlan tag between the same two sites and on the same port at both sites. This is a common provisioning setup.
You could contact your SP and ask if the service could be changed to transparent on both sides. This would remove both the existing services and replace them with one service that accepts any tag you send and delivers this to the other site. In this service your two switchs are setup as basic trunk ports and you can add and remove vlan tags at will.
You can do your own Q-in-Q on top of one of the existing services as you propose. But I am pretty sure you will need to burn an external loop cable to accomplish this. The Q-in-Q Junos configurations expect to drop off the final port to an external interface. And in your case you have two service tags on the same interface to the SP. So to layer the additional vlans on one of these your will need to send them out one port and back in another so this can be combined with the second service tag on the ultimate egress port out to your existing dual service port to the SP.