We thought the whole point of RMS is that it did not need access to the device once it had been enabled
It is. After some failed attempts to connect, it tries the connection less frequently to conserve data usage (it's all explained here). What I suggested to you would make the connection instant. But if it was enabled previously, it should connect automatically, it will just take longer.
If it doesn't connect at all (even after, for example, 24 hours), then that's another issue. In that case, could you please send me the router's serial number via private message?