I see a problem with this approach. One thing I don’t think you can accuse Mormons of is a lack of faith. Holding fast to their position in light of the total lack of archaeological evidence to support the BOM; the multiple substantive changes therein; the demonstrated fraud of the Book of Abraham translation; contradictory accounts of the First Vision; apostasy and condemnation of the original “witnesses”; false prophecies, etc., etc.; they pretty much live and breathe faith. The question becomes, what is that faith based on?
There is what I call the Architecture of Faith, wherein one establishes a factual base (beginning with the concept that we live in and perceive a real, physical world relayed to us mostly accurately by our five senses) and then begins to build a construct of beliefs upon that foundation, each level tied to that which comes before. The mortar that binds these “bricks” is faith, filling the gap between what is believed and what can be objectively proven. There is always going to be some mortar required for any belief (for instance, the belief that while driving through an intersection on a green light, the belief that you’re not going to be hit by a car ignoring the opposing red light; sure it can happen, but the odds are it won’t, so driving through the intersection requires no great amount faith). The important issue is the ratio of faith to evidence; bricks to mortar.
A structure composed of more mortar than brick is extremely shaky and can collapse under very little stress. This is why it’s important for Christians to know why they believe what they believe. An individual’s beliefs may be sound, but if they’re based solely on faith (i.e., it’s what they were taught by someone they liked, so they accepted it), they may crumble in time of testing, or be deceived by whoever shows up at their door carrying a “customized” Bible or other gospel.
In reference to your fist sentence or so, boy, I get that. My lds uncle (former bishop) has a PhD in geology will tell you straight out that there is no anthropological, geological or archaeology evidence to support anything in the BofM or other lds docs, and that is why it is call faith.