I think the DLM is not involved in what you describe is happening.
It sounds like in the small hours of the morning, the noise level increases so much that your modem loses its connection, and it reconnects at the target SNRM, resulting in a lower speed due to the increased noise level.
Later, the noise level falls, which is shown by the currently reported SNRM rising. The modem will not automatically re-connect to get a better speed. The DLM is not usually involved here, although what happened to me once, was that I just left my line alone for a few days when it had happened to connect at a slightly lower speed than usual. At the lower speed, the line was more stable than usual, and the increased stability prompted the DLM to lower the target SNRM, causing it to re-connect at a higher speed than before.
If the DLM did not exist, your line would still drop out overnight and re-connect at a lower speed, and later in the morning, you'd still have the lower speed and higher SNRM once the noise level decreases.