The main reason for the peak flow to happen at a certain time is that the meltwater pulse takes that amount of time to propagate.
If the peak Hoh River flow 40 miles from the source happens at 09:00, one could assume the the flow matches the 4mph that you observed, or that peak melt happens around noon the day before.
At 4mph, then the melt pulse at the source would happen at 09:00 - 40mi/4mph = -01:00 or 23:00 the night before. From 12:00 the day before would make the peak take 21 hours to travel the 40 miles, or about 2 mph.
That differs from the 4mph you observed while floating the mid section.
One explanation could be that the surface water you floated in moves faster than the average flow in the river. That is a common feature what is called "Open channel flow" in fluid dynamics, since the velocity profile approaches zero as you approach to the bottom--the average flow is less than the surface flow.