Based on Mr. Dqdave's observations, I looked at the pipes again. It appears in the pictures that the center pipe has a smooth interior surface and the other two pipes have the raw corrogations.
Allow me to clarify the nature of HDPE pipes. On their own, they are non-weight bearing. Think of them as "cells" that hold open a space in the soil. HDPE storm piping relies almost entirely on the backfill and compacted earth around them for their strength. As an example, drive your 6,000# tractor over one of the pipes...guess what's going to happen. Squish.
These pipes are very different in nature than concrete pipes, for example, which posess their own structural integrity. And they weigh a huge amount more. Backfill doesn't matter nearly as much on concrete pipes and we wouldn't be having the same conversation about careful compaction, sufficient cover, and certainly about them floating down the stream.
All this said, there is a minimal difference between a smooth interior wall (Type S) HDPE pipe and a "raw" corrogated interior wall HDPE pipe. Nearly all the pipe's strength is in the "spiral" of HDPE that creates the pipe itself. The primary purpose for the smooth interior is to provide better hydraulic characteristics so when I provide detailed calculations on a comprehensive storm drain system's HGL (Hydraulic Grade Line), I have a very smooth pipe to work with that can carry more flow instead of a very rough pipe that is more resistant to flow. The interior wall is quite thin and of minimal benefit structurally.
That's the detailed, long, boring answer to the concern. Given the nature of your project, I don't think you're all that concerned about the Mannings Coefficient of Friction of the corrogated vs. non-corrogated pipe. You just would like something that will, well, stay there.
95% of the strength of the pipe in this situation will come directly from proper backfill and compaction around the pipe. Very careful compation to 3/4 up the pipe will really set you straight. And I'm not overly concerned about what you do directly over the crown...you're better off just rolling dirt in there and distributing the load since this is by far the weakest point in the pipe. Beating down on the crown of HDPE pipe in a backfill operation will certainly deform it.