I was once asked about how people in period made hat stiff or hard, and how can we do that easily today. The following is an excerpted from my answer.
Those crazy people probably used just about everything. Wood, straw, wire, bone and starch...Lots of starch!
If you are doing something that needs the starch effect you can NOT get it with the spray stuff. Some of the stores that cater to an older generation might have the boxes of laundry starch that you have to boil. If you can't find that, you could try to boil down cooking starch, but I have never done this and have no idea how well it works. Problem with this is of course 1. bugs love the stuff and may eat or make a home in you hat. 2. If it gets wet, or you sweat a lot on your head it will probably not hold up...get soggy and stuff. Not very pretty!
Another option is to use the fabric stiffeners available in fabric and craft stores. I believe Aileen's in the pink bottle I have used with some success. It is a plastic base solution, like Elmer's glue, which should be a little more resistant to moisture and not attractive to bugs. For both of these you have to sort of mold it as it dries so it maintains the shape. These are not really water proof and will get soggy if exposed to very damp conditions.
All this is really more of a light weight stiffening, for veils and headdresses.
For the really heavier and stiffer head gear, you probably need a layer of buckram in your construction. There are different weights of this. This is a fabric completely saturated with glues to stiffen it. It is pretty plain and ugly to look at, but you cover it with whatever is your fancy fabric. If you were making say a Gabled headdress, you would make the foundation out of buckram, cover the outside with velvet/satin/...whatever and line the inside with satin/taffeta...what ever. When you sew the jewels and decorations on you really only sew through the outer layer (the buckram is a bitch to stitch).
The best resource I can think of off the top of my head is a book entitled "From the Neck Up", although I think a lot of what it has in it is Victorian. It deals with hat construction basics and takes you step by step.
As far as supplies, you can get some pretty stiff heavy interfacing at some fabric stores, but I don't remember seeing any around here. I often just order my buckam from Greenberg and Hammer in New York. I think it runs around $4-5/yd and they have all sorts of other niffty sewing supplies. I don't know if "curtain" buckram would be strong enough, but I guess that sort of depends on your hat! You will also find preshaped buckram hat frames, but they are mostly in bridal shapes. More applicable to Italian Ren.
Anyway....there are the pickings of my mind, for what it is worth!