It looks like the entire project will be going for another two years, but in multiple phases that have subphases with closures of sections of Main Street that will last no more than a few of months each. This is considered "short-term" on the highway=construction tag documentation page (https://wiki.openstreetmap.org/wiki/Tag:highway%3Dconstruction). 

I think the better way of going about this, if we want to avoid the problems cause by moving the highway=construction tags around the street every handful of months, would be to use access=* tags. This requires the effort of tagging each phase correctly, though. I think many people would agree, however, to leave it as primary since road closures like these are more subject to conditions than a project like rebuilding a bridge or paving a new road—but I think it may be better to have which sections are closed properly indicated.