The standard principles of day game apply. If you marry her, you're marrying into a cult, a mild cult as far as cults go, but a cult nonetheless. I have read half of all the comments and decided to skip the rest. It's in the Mormon DNA.
You're walking into a den of crazy, tbm bishop's daughter, I hate to say it but you should really be contemplative about what you're stepping into. On her mind, her eternal salvation depends on marrying a worthy priesthood holder. Also, love how you describe how God has our backs and we can actually act on the notion of things hoped for that are not seen instead of the quaint pseudo idea that all things are known in advance, step by step, and lead to mortal and eternal bliss.
You should take all of the above advice to heart and follow it just in case, so you can make a smooth transition should it ever be necessary. He is not a member and has told me he is not going to convert. You know what the official line of the church is, and what bishops and stake presidents are likely to say. There are other occasions for humor, but these two are off the table.
Maybe it won't be a big deal. However, he was often in a horrible mood after long shifts. Cuddling is not demanding.