We've done it twice, once each way. We took 3 or 4 days and camped off the parkway at campgrounds close to the BRP. The speed limit is 45 most of the way IIRC and you won't be going that fast most of the time. We just took our time and stopped frequently at points of interest.
We did have a smaller Trailmanor TT when we drove it. I beilieve there is at least one overpass that is too low for larger RVs and you would need to detour around. There is an excellent official website that has a mile by mile map of the parkway.
LinkTurn down your computer speakers before going to it.