Well, as I understand it, it's debatable how Cuir Bouilli was exactly made, so we're speculating as to its properties (people have made versions of it, but we don't know what is authentic). From my (limited) reading on the subject, it was most likely similar in rigidity to plate... but I don't think anyone knows, really. Do you any references for it being much softer than plate? I'd be interested to see them.
Considering that immersion in boiling oil generally renders the leather fragile, and in oil under 200°F softenes leather, it's a lame choice for armor. (Oh, the pun-ishment.*) Cuir boulli probably was not in oil. (And boiling untreated hides in oil is how you make cracklins and pork rhinds.)
I've seen and handled a variety of hardened leathers. None of them are even close to the rigidity of even 18 gage mild steel. They do a fine job of spreading impact and reducing felt energy, however. And that's what an armor needs to do. I've personally used water hardening, cyanoacrylate hardening, and hot wax hardening. I've worn baked waxed leather armor, and water-hardened leather. The one experiment I've seen with oil-boiling tanned leather resulted in inedible rhinds...
I've made and used bucklers of 16-18oz stiff moosehide - to get something that can take a blow on the edge, 2 layers, riveted every 3 inches throughout the piece. It WILL stop a swung broadsword... but not in the same manner as a wood or metal buckler. And it will have a nasty gash after.
Pine resin can be used to harden leather; I know someone who does that. It's a bit stiff - but not quite as stiff as water hardened rawhide. Compares to waxing for its effects. Lacquer has similar effects. Cyanoacrylate glue does better still. But still flexible stuff.
Hammering can stiffen leather. Wet it, hammer it, let it dry to shape. This is how sole-leather is made. works best on vegetable tanned, but works with chromium tanned as well.
Rawhide, when wet then allowed to dry in the sun, shrinks and gets stiff. Think doggy chew toys. That's about as good as it gets for actual stiffness of a single layer. Dry edge weighted over a form for best results. The large (1' long) "Rawhide bones" for dogs are enough rawhide for a decent pair of vambraces. (I've worn vambraces made from it.) Once formed, it's best to cold wax it or varnish it. (Hot waxing risks deforming it.)
Oh, the fun things one learns from doing one's own armor work.
In all seriousness, the SCA and several other recrudescence groups are doing a lot of experimentation, and working from a lot of period recipes. And getting materials with the promised qualities. None of them approach the rigidity of metal. At hardest, think plastic buckets of similar thickness.
Oh, and if you have a dog's rawhide "bone" to hand, and need a cast, soak it in hot to the touch water (about 120°F) for about 20 minutes, then undo the knots, and unroll it, wrap it around the limb loosely, pin it, and let it dry. It shrinks as it dries, so don't do it tightly.
Oh, and Alaska Natives spittle-and-chew harden boot-leather... and you don't want to think about their tanning process...
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Some good reads on the matter:
http://www.personal.utulsa.edu/~marc-carlson/leather/hl.html
http://www.jeanturner.co.uk/static-content/tutorials/CuirBouilliTechnique.pdf
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*a lame being a strip of leather or metal used in articulation points of armors.