The definition of faith you ascribe to me is not my position at all, but I am not offended that you said it.
Kishkumen, I am glad I have not offended you and I am sorry if I misrepresented what you think. I made sure to say "It seems that" rather than it is, but if this did not come off clearly I am again sorry. An internet board is hard to put subtleties into clearly and I realize now that I failed at this. Thank you for your tolerance of me
Tobin: The witness of the Holy Ghost is not evidence?
Ignoring facts over that special feeling is great when the facts don't support you. Of course though that special feeling didn't come with any interpretation. You had to give it that. How do you think a Catholic will interpret theirs? Reason should not be ignored when it comes to the facts available.
I think both good Catholics and good Mormons will try to interpret them correctly. Mormons and Catholics that are not truth seekers will not care and will continue to believe what they desire to believe. I am a truth seeker and I'm sure many Catholics are as well. Spiritual experiences are so varied and happen in so many circumstances that it really isn't as simple as "I pray and get a spiritual experience; therefore, my religion is true." Neither sophisticated Catholics nor Mormons believe this. I was just reading an article about how they elect Popes from Time. Perhaps you should check it out.
The problem is if it's not true then you have to agree you cannot have faith in it by the definition you gave.

That is not true. I'd have faith in something else and I may not call what I feel the Holy Ghost.
Prophetic infallibility (doctrinal infallibility) has ALWAYS been the essence of Mormon Doctrine. It is only Mormon apologists that deny this.
Really? Because I can pull out several quotes from Joseph Smith, having just read his Journals about this. There are quotes (like in the Polygamy manifesto for instance) which preach that Prophets or the majority in the twelve, etc, are infallible. If they are infallible though, infallible prophets led me astray in believing they were fallible as I read their writings; therefore, they are fallible. Here's one such quote:
"If we are faithful in all things, for we are even entitled to greater blessings than they were, because the[y] had the person of Christ with them, to instruct them in the great plan of salvation, his personal presence we have not, therefore we need great faith on account of our peculiar circumstances and I am determined to do all that I can to uphold you, although I may do many things <invertaintly [inadvertently]> that are not right in the sight of God; you want to know many things that are before you, that you may know how how to prepare your selves for the great things that God is about to bring to pass" Joseph Smith's 1835-1836 Journal, Pg. 31-32, November 12, 1835
Sorry, the reply on prophetic fallibility may have come across a little strong. I am sincerely trying to be respectful and I do respect your views.
Now I will try to address everything else.
One common mistake that I find that New Atheists and other skeptics make is that the Holy Ghost is merely a feeling. Maybe that's what you thought it was, but then if that is the case then I really do understand why you don't believe. For me, and others I have talked to that I know very personally it has always been more than that. I have sensed the Holy Ghost, I have sensed his presence, I have heard his voice speaking for God, and so have many others. Sure you can just assign it as "emotion" or "hallucination" but I can substitute eyesight for sensing the Holy Ghost and you could make exactly the same arguments. It is a sense in the real term, something that scientifically minded people like you and I should be more than open to given that we know of something like 20 different human senses now. More from neuroscience are being found all the time.
Suppose you say, as you have that the fact that say Catholics and Mormons in large part got different answers (unsurprising given that they have committed their lives to different Church's.) Suppose you say this casts doubt on the epistemology of revelation. Well you're right, but the epistemology you chose isn't any better. No epistemology is good, except perhaps direct observation (sensing the existence of holy ghost or seeing a tree.) Let me substitute Science.
Science believed set x of things in the year 1850. Science believed set y of things in the year 1950. Science believes set z of things in the year 2015; therefore, Science is worthless and untrue. It is true that science changes but this does not mean that I personally just decide to discount science completely. I look at what is in conflict and what is not, and compare. Some things are obvious. Evolution for example, both micro and macro has been observed. Similarly things like the existence of spirits, the golden rule, an afterlife, and other aspects of religion are for the most part universally agreed upon by spiritual religions. These are immutable aspects, and they comprise many of our core doctrines.
This brings me to my distinction between spiritual and scientific experts. Religion and Science can be seen as a Venn diagram. Science makes claims that religion does not conflict with in which case we trust science. Religion likewise makes claims that science does not conflict with. Each of these claims are made by experts in their fields. Our Prophets and the Pope and Cardinals to some degree, and other spiritual experts compose the spiritual side. These spiritual experts agree and disagree on various things, but similarly have much in common. Then there are scientific experts, people who spend their life studying public data and reasoning and experimenting with it. They disagree on many things, but some things are clear to them. Both of these experts take valid, but different avenues to truth, have their share of things they are wrong about, and are fallible. When the two collide I almost always take the side of science. That being said though I don't necessarily believe that they are wrong. I just take science's side. As I said before Science can change and so can Religion. I honestly think it is impossible to know which things the two sides are right and wrong about, so I make a utility bargain. I find science much more useful to believe about, for example, the historicity of something or the creation because science allows for technology. Religion does not, but provides for salvation. Given that disbelief in the historicity of the Book of Mormon is far from something that I could be banished to outer darkness or even the terrestrial kingdom for, I chose science. I would also point out that this reliance on spiritual experts leads to degrees of certainty. I am much more certain about non-religion specific claims. Then comes Christ, where I become less certain, after which comes Mormonism which I am even less certain of. As such I try my best to not be dogmatic about any of my views. Hopefully I have fulfilled this goal.
Sincerely, Lolitsme