I've dealt with construction zones on numerous occasions. Each situation is unique. Sometimes I've ridden through them just like any other vehicle - and "taken the lane" because that was the safest and most appropriate measure. Other times I've been able to ride inside the coned-off area with caution... A couple times I've gotten off and walked around the construction zone.

From your description, I'm guessing that this is a 2-lane highway with no nearby parallel alternative. I'd ask the flagman or whoever seemed to be in authority at the entrance of the zone what they'd recommend. Sometimes the actual work is only being done on a small segment of the closure, but there can be pickups and larger equipment just flat-out flying around in the cordoned-off space. Plus there can be sudden drop-offs and exposed trenches. It might look benign... You just never know.

Some pretty experienced cyclists have died traversing construction zones... Care is the watchword.