It sounds like a moot point. It's not possible to acquire the extensive experience necessary to have intuition without having another strategy in the first place. Intuition is the long-term consequence of employing a strategy: no longer having to step through the same sequence every time.
Exactly this.
Indeed intuition is needed. When John Nash, a Mathematician with schizophrenia, was asked why he believed such irrational things when he such a brilliant man, he responded along the lines of "Those irrational ideas came to me the same exact way my rational, ground breaking ideas came to me." So intuition will always be needed, we just need to remember to check it.
On the other hand, I don't see how you can keep experience and intuition from being a factor in any instance of the scientific method.