Leaf lard would work for soap, it would make a slightly softer bar than backfat would. If you add in that coconut oil you'll get a firmer bar. Curing it for several weeks will help too. Lard soap is so lovely.

Ther is a website called "soapcalc" that helps with lye proportions and has a dizzying and inspiring list of fats.

Balm of gilead is one of my favourite things. Cottonwoods are one of the trees I'd always been able to identify by smell in the dark. They're so lovely.

The saponification process pretty much takes the meat smell out of the lard, yes. I had one batch turn out weird once but I think I may have scorched that lard. I've always done cold process, so yes, I heat my oils altogether to 120F-ish and cool my lye water to 120F-ish, combine them with a stick blender until trace, add my grit (I always use ground apricot seed or walnut shell) and additional oils/scent, pour into molds, remove when hard, cure for... honestly I do about a year and a half to 2 years at this point, which makes amazing soap, but anything more than six weeks is nice.

I've never used shea butter, if it's for moisture I might add a little of it after trace?

Let me know how your experiments go!