A few points addressing the core issues as I see them.
Soap Hardness: Who cares? I can make pucks from 100% KOH soap, I cannot think of any other reason to want shave soap to be hard. We want shaving soap to perform on the face, it does not need to last in the shower. I prefer soap made from 100% KOH so I skip the drama of using NaOH and KOH together.
To me 100% KOH creates a soap with more of the shaving performance properties I want. Certainly that's subjective, but what's not is there is more complexity to using two lyes. If it's not needed, why bother? My favorite commercial soaps are KOH only.
Some soapers I respect very much use two lyes and they have their reasons. I just don't understand them.
Salts and carbonates and Bears, oh my! As I said above I don't believe a shaving soap needs to be as hard as a bath soap. It needs to be able to be packaged and that's it. A large number of learned shavers use soaps that come in tubs; these are called "croaps". This is a portmanteau of"cream" and "soap" because it has properties of both. It can often be easily molded, but it is loaded on the brush just like a soap is. The hardness ranges from Dove bar to cream cheese.
Cella is the archetypical Italian croap. It's packed in a tub typically, as are many/most other croaps. Arko is a (I think) Turkish croap that comes in a stick form. It has polarized wet shavers; I'm personally not a fan but for the price and performance it's hard to beat. I'm just not a fan of the scent. Some people call it citron, I call it urinal puck. Anyway, if you are getting something from Amazon anyway, grab a stick of that someday to check out and compare. It performs incredibly well.
Anyway, that's a long roundabout way to say your shaving soap does not need to be as hard as a bath soap, and you can have whatever form you like with a 100% KOH soap. It is completely acceptable, and even desirable, to package shaving soap in a tub/tin.
I
do add something which does make the finished soap harder, I use Sodium Lactate. I add this because it makes the soap easier to handle when cooking. For some reason unknown to me it makes it smoother and easier to stir while hot, and this makes it easier to mold. When cooled it seems to be quite a bit harder, but not so hard that it does not load the brush properly. It also looks creamier when done and loaded in the tin. I have a picture of "plain" soap, and soap to which I have added lactate and Titanium Dioxide here:
http://www.silverfoxcrafts.com/2015/12/basic-or-bedazzled/
If you are selling soap (or intend to), the difference will be interesting.
Curing: A hot process shaving soap will exhibit most of it's finished properties right after cooling. My own process does not rely on a cure to dry the soap to increase hardness in any way. I did say "most properties" though. As DeeAnna says there's that change in the molecular structure within the soap that still happens as it cures. I'm sure there's a dissertation or at least a thesis in there for someone to figure it all out. My own experience tells me that there are declining improvements after 2-4 weeks. I try not to give shave soap away that's less than 2 weeks old.
So there's my $0.02, worth what you paid for it. Am I opinionated? You betcha. Any wet shaver who also makes his own soap will be opinionated.