Am I understanding correctly?
In your own home, you tried connecting the HG612 directly to the test socket of the NTE5/A via a micro-filter and it did not synchronise? (The Power LED was solid green, the DSL LED was flashing green?)
You have also taken the HG612 to a different address and connected it to the line and it did synchronise with the remote DSLAM/MSAN?
If the answer is "yes" to both of the above questions then it tells me that there is some sort of fault, possibly with the NTE5/A, in your home.
Synchronisation of the modem with the remote DSLAM/MSAN must occur before any attempt is made to authenticate. In the case of
Openreach's GEA-FTTC product, using a separate modem and router, the authentication is managed by the router.