The best theory I've seen for the model's construction was put forth by Daren Dochterman over on The Replica Prop Forum (his most specific posts about the construction (link)
and images to support his idea (link)
). His thought is that it was made of "gaffer's foil" (the foil used on film sets to shape light or make improptu flags) wrapped blue lighting gel material. This would have allowed a small stage light to have been put inside it. Shaw also chimes in on the possible use of the Catspaw 3.5" metal Enterprise in the episode. Here's the full thread (link).
Looking at photos, you can see the foil-like texture and these odd strips that look like tape folded around the maw.
It's not a windsock dipped in concrete, that's pretty clear.
I'll examine those links when I return home. (Something is causing the browser to "crash" when accessing here at the office.)
Thanks for the informative (and some humorous) replies so far!
Those links are using "therpf.com" not "thereplicapropforum.com" URL they've been using since their main domain got kidnapped and held for ransom a month or so ago.