Which is the best way to interface all disciplines while adhering strictly to implement QMS during the construction phase?

It is the first step to adhere the QMS: GAP ANALYSIS the detect the physically implemented system compared with the standard requirements.

Communication is key.  First after gaining input from all, a plan can be formed, and agreed upon.  Next the plan must be followed and, with the constant feedback of all, adjusted for issues and irregularities.  These will almost always occur.  It is important to weigh the concerns of all, and weight the concerns based on the best advice available, not just going with the loudest voice.