I think maybe the brads are fine also.  The only other thought I had would be to use something like double stick tape to connect the two together.  I think maybe if you used a small piece only at the side it might show up on the shadow itself so you might have to find tape large enough that you could cut the entire head shape out of.

The brads do not appear on the screen; they will blend in with the rest of the shadow. (Even though the plastic is white, the shadow is a dark grey if not black) The most I've done is hold it up in front of a light and looked at the shadow on the wall, but it seems satisfactory. I was a bit concerned that holding down only four edges wouldn't remove all of the floppiness and you'd see a gap between the two layers, but it shouldn't be a problem if the puppet is well-rehearsed.

Shawn, I'm ahead of you: I have some mounting tape for testing out attaching 'dialogue' pieces. These are going to be cut-out words or symbols which can be attached to the puppet ... but removable :D
But I didn't want to head that way because it lacks the overall professionalism of the rest of the design; and I wasn't sure of durability.

The brads have now grown on me, and I think this proves an important point of puppet design: sometimes that easy solution you've been avoiding is the one you should be using!

Now that I've solved this, I'm moving on to figuring out whether I want more articulation or not.

Thanks for the feedback guys - always valuable!

Na, I'm afraid I can't contribute much in terms of the design - I've not heard the term 'brads' before but if it helps, looking at the two images, as a novice, I can see little difference between the two. The design is brilliant! I'm so glad you were able to make it work 

Thanks Lizzie - I'm really happy using this fix now, and should be able to order materials next week and start selling them soon.

Brads explained:
http://en.wikipedia.org/wiki/Brass_fastener

PS. I'm not ignoring the other thread on purpose, just been distracted with work. I'll take a look at the pics and vid asap.

Yay for some sales! I'm still really keen on a School of Puppetry Collector's Puppet!

I had a thought. Have you ever worked with flooring plastic? I bought some recently. It's the plastic used under runner mats etc in people's homes. It's quite thick (could be tricky to cut with detail) but is very strong whilst still being malleable.

Thanks for the brads link. I feel a little silly now! Having looked again, I couldn't really distinguish the brads. Awesome design Na!

Yay for some sales! I'm still really keen on a School of Puppetry Collector's Puppet!

Yes, sales would be lovely. I haven't produced any new puppets for sale in over a year, so it would be great to get back to it.

And a little correction: this will be for sale under 'Puppets in Melbourne'. It's confusing I know, but SOP is all about articles/tutorials, PIM is all about actual puppet products. So this won't be sold via SOP at all.

I had a thought. Have you ever worked with flooring plastic? I bought some recently. It's the plastic used under runner mats etc in people's homes. It's quite thick (could be tricky to cut with detail) but is very strong whilst still being malleable.

No I hadn't - that's actually a pretty interesting idea. Wonder how expensive that would be ....

Thanks for the brads link. I feel a little silly now! Having looked again, I couldn't really distinguish the brads. Awesome design Na!

That's ok. For some reason I don't think the name is well known, a lot of people I know don't know what they are either. Maybe it's because they're mostly used for scrapbooking and that's a pretty niche hobby.

I'm not sure what you would consider expensive but I thought it wasn't too bad. Can't remember exactly what I paid though and the stuff I purchased wouldn't suit your needs. It had the teeny spikes on one side so it attaches to the carpet which works just as well attaching to foam. But I saw some there that was smooth both sides. It isn't coloured but you could easily paint it if you needed colour.

May not work, but worth checking out.

Expense isn't the only problem too - it's the weight. But anyway, I have a good material for the time being, so I'll keep flooring in my back pocket as a backup idea if I need it.