That's exacty what I'm saying. Irrationality has it's place. Sometime's it's best to use it. But it's dangerous to start calling a method that is based on irrationality to be "rational". Call it justified, call it "the fastest way", or call it "better" (as I did).
In a discussion such as you are starting, the biggest problem is definitions to avoid talking past each other.
Irrational is not quite what I think you are after. Maybe a new word and definition could be coined by you for where it is you are wishing to take this after establishing your premise.
"not rational" "a-rational" etc
Otherwise you will start a discussion in semantics. The more precise the definition the better you will be communicating your thoughts.
An irrational approach would take a "best guess" at the rocks/currents/water ahead and get to the island. The risk for loss of both ship and life are there. The movement ahead before checking it to see if you can actually make it is irrational.
I would say as a counter to your use of the words rational/irrational that the best guess is a rational approach within the constraints of time allowed to make shore. They would explore the shoal for the best passage within the time constraints allowed.
Maybe what you are saying is that in certain arenas science does not provide a definitive answer. I don't think that is debated by anyone. Chaos theory establishes that fact in certain situations. QM establishes it also for certain kinds of knowledge.
You may have to move toward your conclusion before encountering an issue upon which there may exist some debatable topic
if "remaining in control" is a priority, anyway.
Control or prediction is the goal of scientific knowledge, but in most areas the limitations imposed on that possibility are also understood where they are fundamental in nature.
Irrationality certainly can be better
Again a semantic issue. I think you are saying that a complete solution is not always possible. This does not make the evaluation irrational however.