At the risk of sidetracking you, it so happens that I picked up one of Craig's books on the resurrection last week and was surprised to read what sounded like his views on 'experiential.'  (I still haven't looked at the Craig link you gave me.  I've relied only on your quotations).

From the preface I read:

In point of fact we can know that Jesus rose from the dead wholly apart from a consideration of the historical evidence.  The simplest Christian, who has neither the opportunity nor wherewithal to conduct a historical investigation of Jesus' resurrection, can know with assurance that Jesus is risen because God's Spirit bears unmistakable witness to him that it is so.  And any non-Christian who is truly seeking to know the truth about God and life can also be sure that Jesus is risen because God's Spirit will lead him to a personal relationship with the risen Lord.  Thus, there are really two avenues to a knowledge of the fact of the resurrection:  the avenue of the Spirit and the avenue of historical inquiry.  The former provides a spiritual certainity of the resurrection, whereas the latter provides a rational certainty of the resurrection.  Ideally these ought to coincide, the Spirit working through the rational power of the evidence and the evidence undergirding the witness of the Spirit.  But even if the historical avenue proved inaccessible, the avenue of the Spirit to a knowledge of the resurrection would remain open and independent. [Preface to The Son Rises]

Now, the problem is that you have distilled this into Craig asserting that 'you should pray.'  This is to reduce God to a cosmic vending machine.  No doubt there are Christians who act like that and no doubt there are a host of atheists that will only believe in God if they receive from him exactly what they demand of him.  I have underlined an important component to Craig's argument- the personal relationship. 

Craig may very well suggest prayer, but he will also take into consideration that what is at stake is a relationship.  In a relationship, making strident demands is no way to get what you want.  This is especially the case when the object of the relationship is vastly superior to the other.  The President of the United States is not going to give you an audience just because you demand he do so.  Moreover, even if you are granted the audience you will likely have to undergo background checks, leave your weapon at home, and give no indication that if you showed up in the Oval office you were just going to spit on him.  But God is much more superior than even the President.

I have a hunch- and of course, I'm not a Craig scholar and expert like you are- that if you were going to ask Craig precisely how you should invite the Spirit to assure you of the resurrection (ie, the resurrection, not God's existence- as if that's all God cares about!) he may eventually, in fact, it is safe to say he certainly would, suggest prayer.  But in the lead up to that I think he would talk about proper expectations, proper approach- ie, certain humility- a certain willingness to be teachable, etc.

If you prayed to God for proof of his existence and he said "Here I am, the Christian God" and you said "I hate you, Christian God, look at all of the abuses you've done!" trust me, you're in a worse spot then you were then if God hadn't answered the prayer at all.  Job's response was better (though he didn't contest God's existence).