If your interleaving depth stays at 1 when your speed drops to 60Mbps, then that indicates DLM is *not* intervening in your line.
Your change in SNRM is therefore more likely to come from an increase in noise - from what you say, it is around 5-6dB of noise.
But we can't say what the noise is; it could be crosstalk from another modem that is being turned on/off. Or from some other source of noise - heating, fluorescent lights, motor, factory, shop, sewage pumps etc. The best way to distinguish would be to figure out the pattern of on/off changes - either manually, or by logging 24x7.
The differences between the bits/tone (or SNR/tone) will likely tell you what tones are being affected by the noise. As Kitz says, 6dB is likely to be 2 bits per tone, on average. Again, the actual pattern of loss over the full spectrum might give you some clues about the type of noise.