Dagwood,
The tunnels have an arched ceiling and the chart linked below shows the maximum at the middle of the arch along with the minimum clearance at the roads edge. You should have no problem getting through any of them.
I've traveled the entire Parkway from end to end many times over the past 35 years and they're not an issue. Just don't hug the road's edge on the two that have minimum clearances of a little over 10' and you'll be fine.
Click for
Parkway Tunnel Clearances.
Linear Mode
