Fundamental purpose of Project Management is to deliver what your clients want at a specific time. Effectiveness you have mentioned depends on the requirement and tolerance of clients.
All clients want developing team finished within one month and everything. But they seldom do not know what feature is the most important. From my experience, we use Scrum to address which features must be presented and usable first. Mentioning first, then , final phase to clients is the way to make them know we propose agile development methodology and urge them prioritise the deliverables.
Before providing the value judgement or proposed methods to combine the methodologies from the management point of view, we have to figure out the budget, time constraint and possible market competition. OP has to mention more about.
As for quality of work and communication issues, it is difficult for us to judge because of the discrepancies among working cultures of team members.