My only claim is:
(a) Christian belief is possibly true in the broadly logical sense;
(b) Christian belief includes IIHS, which, if true, would be a reliable belief-producing (cognitive) mechanism; and
(c) If (a) and (b) are true, Christianity is rational.
If the instigation of the Holy Spirit were (a) known to exist and (b) known to be a reliable source of information, then a belief in Christianity would be rational. Since the instigation of the Holy Spirit is not known to exist and it is not known whether it would be a reliable source of information if it did exist, a belief in Christianity is not rational.
So if our question is, "Is it rational to believe in Christianity," the answer must be "That depends." On what? Clearly, on whether it's true. If Christianity (including the story about IIHS) is true, it's rational to believe it, in the absence of defeaters, via IIHS. If it's false, it's probably not rational to believe it because the only way to rationally believe it would be through the use of publicly available information.
Since it is not possible to know whether Christianity is true, it is not possible, even under the terms of your own convoluted argument, to know whether it is rational to believe in Christianity.
You claim the instigation of the Holy Spirit as your means of knowing Christianity is true, but you know very well that many Christians have claimed on the same basis (and other believers have claimed on an empirically indistinguishable basis) to know things are true that are flatly contradictory.
Allen claims to know through the instigation of the Holy Spirit that the Pope is the Vicar of Christ on earth.
Bob claims to know through the instigation of the Holy Spirit that the Pope is the Antichrist.
Charles claims to know through the instigation of the Holy Spirit that gifts of prophecy and speaking in tongues passed away after the first century of Christianity.
David claims to know through the instigation of the Holy Spirit that the gift of speaking in tongues continues today, and is a sign of the fullness of the Holy Spirit.
Ed claims to know through the instigation of the Holy Spirit that Christ does not want his followers to take foolish risks.
Frank claims to know through the instigation of the Holy Spirit that Christ wants his followers to demonstrate the truth of the Gospel by handling serpents and drinking strychnine.
It is thus obvious even to the most casual observer that a belief that one is influenced by the instigation of the Holy Spirit is not a reliable source of information. Having no reason to believe in the reliability of the imagined instigation of the Holy Spirit, we have no rational grounds to consider it as a reliable source of information.
Further, your argument for the rationality of Christianity, or a very close parallel to it, can be offered in defense of absolutely any irrational belief.
Further, your definition of a basic belief is flawed, and even that flawed definition is applied to faith in a flawed manner.
A basic belief is properly a belief that can reliably be believed without evidence. The belief is self-evident or self-proving. Religious apologists have attempted without success to extend this concept beyond beliefs that are self-evident or self-proving, to any belief that is formed by means other than evidence and reason. However, if we define a basic belief as you do, then whether a belief is basic has no bearing on whether that belief is true. A basic belief as you define it may be useful for forming quick, ad hoc impressions, but is no use whatever if we decide to carefully investigate whether something is true.
You think you see a sheep across the road. You hold this to be a basic belief. but your belief that there is a sheep across the road is not, properly speaking, basic. It may turn out to be a dog that looks something like a sheep. Your perception is subject to error. However, some people in your area keep sheep; you have seen sheep before, and it is not altogether unlikely to believe that there is a sheep across the road. Seeing a sheep across the road would not be a remarkable occurrence. You conclude that there is a sheep across the road. This belief is not irrational, despite the fact that it is not a basic belief and is not known to be true. There are, as well, a number of different ways to test this belief.
Suppose, on the other hand, that you think you sense a unicorn across the road. You cannot see it, hear it, or smell it, but you perceive in an inward and ineffable manner that there is unicorn across the road. However, nobody in your area is known to keep unicorns, there are not known to be any wild unicorns living in the area, and in fact, nobody living has ever seen a unicorn anywhere at all. Nevertheless, it is theoretically possible that unicorns exist, and if they exist it is theoretically possible that there is one across the road. It is also theoretically possible that you have some unusual gift of super-perception that allows you to perceive things by other than the usual means. If there were a unicorn across the road, and if you had such a gift of super-perception, it is possible that you could perceive the unicorn across the road. A thorough investigation reveals no evidence of a unicorn, but you continue to perceive the unicorn. Since it is not possible to prove that unicorns do not exist and it is not possible to prove that you have no ability to perceive unicorns, your belief that there is a unicorn across the road is indefeasible by any rational means. There is no way to test the belief, no way to test your claimed gift of super-perception, and no way to test your belief in the unicorn.
Are your belief in the sheep and your belief in the unicorn equally rational? No, they are not. A rational belief in the unicorn requires, at the very least, further investigation. It is reasonable in this case to remain skeptical in the absence of further evidence.
Now, if you go about telling everyone that there is a unicorn across the road and that you have perceived this unicorn yourself even though others can detect no evidence whatsoever of a unicorn, many of your auditors will form the belief that you are mad. They cannot know for certain that you are mad, but many people have gone mad before, and it is not altogether uncommon for a person to go mad. They can see that you are behaving like a person who has gone mad. It is altogether more likely that you have gone mad than it is that there is a unicorn across the road. Their belief is every bit as rational as your earlier belief that there was a sheep across the road, and far more rational than your later (and indefeasible) belief that there is a unicorn across the road.
Admittedly, a person who wants to argue that psychic powers actually exist will have to mount an argument, and surely evidence would be required to make such an argument.
And the same is true of the instigation of the Holy Spirit.