Harmonise (or harmonize) means to make (one thing) compatible with (another); (ref, #4).
The word has come into common usage with respect to reconciling or coordinating laws and tariffs, as described in this wiki article on the harmonization of law.
This document discusses the harmonization of accounting practices.
The Business Dictionary generalizes this to be
the adjustment of differences and inconsistencies among different measurements, methods, procedures, schedules, specifications, or systems to make them uniform or mutually compatible.
Another source has a similar definition:
Generally, harmonisation can be defined as “actions or processes that through matching and blending bring about agreement, reconciliation or standardization”.
Harmonisation is also used to describe the reconciliation of dat or information, as this source indicates:
Harmonization is to create the possibility to combine data from heterogeneous sources into integrated, consistent and unambiguous information products, in a way that is of no concern to the end-user.
Harmonise has become a buzzword in some circles, especially within the European Union and its governing bodies. So...
If you want to use something a little closer to the vernacular, you can try unify, which means to combine, merge, fuse or coalesce, to resolve conflicts and bring together into a single or common framework.
But I think coordinate or synchronize will be understood very well by anyone when it comes to unifying the common view of what the status of a project might be.