The foam mat probably won't work for you for a few reasons: it's not an easily-workable material, you're working from scratch, and its properties do not match those of your intended end. Peter's animatronic Elite used it because it roughly matches the consistency of the Elite's skin, he knew how to work the material, and well, it was a large, curvy project. In my experience, you can't get any sharp corners in it.
As for the garage note, if you're working by the garage door, there should be no problem, if it's partway open. Maybe, I just have a really big garage, but whenever I work, and I move to the house side of the room, I don't even smell it. And Urethane is strong-smelling.
Well, the sad fact of the matter is that there are hurdles when making high-quality armor. You could make cardboard armor. It's very cheap and non-toxic. But, let's be honest, that's neither great quality nor durable. (No offense to any of you cardboard armorers. I'm saying, typically) If you're good with clay and figuring out what something looks like in full scale in real life, you could make a clay form and buy expensive casting supplies, make a mold, and cast. This is really expensive, not the most durable, but probably the highest quality, and with the added bonus that your mold can be used to cast more, which you can sell.
Then, there's pepakura. It's pretty cheap. Download the free version of the program, buy some cardstock, resin, fiberglass, bondo, some Elmer's, and a respirator, and you have your basic needs. I'm sure you can find a place to work. As long as it's outside, and relatively away from people, and you make sure to wear a respirator, you're all set.
I'm not gonna say it's the only way. I'm just saying it's the way I prefer, and that's why I prefer it.
And, Nintendude, you're right. Sandpaper and a power sander are necessary. The other thing I forgot is rubber gloves. Latex, be sure. Nitrile and other types of gloves are too cumbersome. They're all fine for working with resin, but only latex is form-fitting enough, and flexible enough, in my opinion, to work well.
And, the reason electronics are easier than structure is because it's easier to string wires and components together than build complex papercraft or sculpt detailed forms, and make a hardened plastic (or glass-reinforced plastic) prop. I mean, I had fans, 3 batteries, and a potentiometer, and the wiring was easier in my helmet, than the actual build. Hell, even painting was harder.
