Jumping in here for a moment...
(I'm actually Beyr's GM)
I, granted, am new to running the Dresden Files RPG (and the FATE system in general) and since he's seeking information for the group I'm going to need page quotes before I can make a final decision here.
I'm slamming into a couple problems:
Tedronal, you made the statement:
"Glamours (and Greater Glamours by extension) act neither as evocations nor as thaumaturgy. They are simply what they are."
While it is nice to say this, and technically you are correct as far as thematic reasoning goes, as far as game mechanics however that is a completely different situation.
According to the information in "Your Story" the heading under "Glamour" gives no rules, nor does it say that it does not follow the standard rules for "Veils" which are laid out on page 276 of "Your Story" this leads me to believe that a player character with "Glamour" can use glamour to create a veil as per Evocations.
Which sends us to "Your Story" page 255 - Utilizing the side bar found there we see the system for veils.
Thus, not only do they cause mental stress, as per any spell casting, but they do it in the exact same way. You spend your power, you take your hit, and you move on. Remember, in the books Harry also doesn't get mentally winded every time he hurls a spell either. He's done some pretty impressive things without seemingly taking any mental stress. Game mechanics however work differently.
The reason why characters wouldn't take (as much) noticeable stress is because Veils take a smaller amount of power than other uses of power and because they last until pierced.
So, whereas Harry will (in the books) have to cast 3-4 spells before getting winded (which when we look at this game that means, assuming he is using rotes) around 3-4 mental stress total. A veil, which is kept up for however long the scene is, would only require one activation and would only cost effectively 1 "power" and thus only 1 mental stress, thus only accumulate 1/4 as much mental stress.
As to the game itself the question becomes, "Well then what good is Glamour?"
Well, for one thing, Glamour is cheap.
At a total cost of -2 Refresh Glamour is a bargain.
As it can be used for veils, it seems to indicate that it can be used for Evocation style veils. As such though it would follow the same rules, and would still generate mental stress. The main difference here is that you use a skill, and not "power" to determine the strength of the veil.
Not only that, but it allows the creation of a "seeming" which allows you to change an appearance (a power not mimicked in Evocations or Thaumaturgy) as a non-stress causing action. This allows you to simply make a defense or block roll against attempts to recognize the seeming.
The biggest benefit of the Glamour is that you don't have to concentrate to maintain it.
The main reason we don't see Fae usually winded from this is because we rarely see the Fae throw down in the novels. They usually have agents that do things for them (such as Harry's Faerie Godmother's dogs) or we are seeing ridiculously powerful entities like the Summer/Winter Ladies, the Queens, and other True Fae.