We load the rod in the primary frequency and then unload it in the secondary frequency.
Carl,
I don't know how you could determine which mode is in play as the rod unloads but I don't think the relative amplitude of the second mode is very large compared to the amplitude of the first clamped-free mode, or as Merlin has suggested the first free-free mode. The residual second mode shape that you see at RSP1 is quite small.
As I understand it Merlin's model only deals with first clamped-free mode and it seems to give a close estimate to measured tip speeds. That fact would seem to argue that the rod is unloading with a dominate first clamped-free mode, but Merlin may have some more recent results that favor the first free-free mode.
Your Trebuchet system is very interesting and may be a way of getting the node of the first free-free mode to move near the hand as Merlin has been
investigating in this reply to Chris Korich on the relative mass of the reel in regards to the "feel" of casting (whatever that might mean to different casters).
"The best way to cast a rod is to take the reel off and out it in your pocket"
When it comes to producing the highest amount of angular acceleration for a given amount of torque applied in distance casting I think that would be true because the MOI of the reel could be quite significant when the rotation center of the caster is near the elbow at MAV.
With that in mind, Renee Gillibert is famous for the cardboard reel he made to comply with the ACA rules that requires a reel that can hold all of the line is attached to the rod in the single handed distance game. I would expect that rule is there for a reason.

Gordy