Mormonism is seen as a "cult" by evangelicals who are the hardest of the hardcore of the GOP base. A great many of them want nothing to do with any Mormon and several stayed at home. Even those who did vote for Romney were sub-enthusiastic about it. The secularist moderate Ryan did not help any. How does having a real evangelical TP running-mate not help at least somewhat?
I don't really think any candidate was going to overcome the "war on women" narrative that hung around the GOP's neck for all of 2012 (or, from October onward, the perception that a nutty Islamophobe's video was responsible for the murders of four Americans overseas), but Romney didn't do much to give himself a fighting chance by playing-it-safe.
Mormonism as a "cult" had certainly played a role in the primaries, but most of the religious right (especially the leadership) had rallied to Romney's side by the general election; you note he won the traditional Red states handily. He might get a little boost from marginal increases in Evangelicals, but it will be small, and almost certainly outweighed by losses from strengthening the "War on Women" meme (as almost any candidate from the religious right will have past statements or ties that can be mined for that). The cliche about "Democrats fall in love, Republicans fall in line" was still quite operative in 2012.
Paul Ryan was a perfectly serviceable VP, and actually generated some positive press (which Romney needed). He was reasonably well respected across most of the Conservative base (note how he was considered an acceptable compromise candidate as Speaker by most Republican factions during the recent Speakership kerfuffle).
The biggest changes for replacing him will be: a) whoever was chosen probably throws their hat in the ring for 2016 (or is stronger, if it's someone currently running) and b) Paul Ryan, without the exposure, doesn't end up Speaker of the House.