I survived a non-loaded ~44 mile parkway ride on my 39/26 paramount. Parkway road grades are generally not very steep, but they can be unrelenting. Here's a short quote from an environmental study of parkway construction:

"Role of Gradient: Vertical gradient is related to
location. BRP gradient had a significant role in
environmental impacts. The designers followed
established parkway precedent in insisting on gentle
vertical grades conducive to a pleasant, safe and easy
driving experience. A gradient of 3 - 6% became the
BRP standard, with an absolute maximum of 8% for
distances of ¼ mile or less. (Lord, 1954)"

Another thing to consider for your trip is to have good front and rear lights - some of the parkway tunnels are quite long and curve such that you can't see either end when in them - very scary without lights.