The DLM system that runs on FTTC services will increase the target noise margin to compensate for issues
DLM used by FTTC does *not* alter the target noise margin, ever. It uses different tactics. This is a different variant of DLM, and is considered more "modern" and more suitable nowadays - but how it will work in your case will be interesting. Sorry - I can't remember the names of the two variants at the mo.
The first interventions usually involve turning on FEC and interleaving. If these aren't enough, then the amount of FEC can be increased, and the "spread" of interleaving can be increased.
If these interventions still aren't enough, then DLM reverts to the next stage... which is to limit the sync speed, also known as "banding".
That last type of intervention will reduce your sync speed directly - and as a consequence, your SNR margin will lift.
If this banding isn't enough, then you may get banded to a lower speed, with higher consequent margins.
Openreach don't allow ISPs to alter margins, or to reset the DLM system. They *do* advertise that the line can be set to one of 3 "stability" levels - which alters the threshold values used by DLM when deciding whether to intervene. However, I haven't come across a single case where this setting has been altered - or where an ISP has even indicated that they can make this change.