First, I think that you should do one or more prototype/template out of paper or card to fit your shoulders. Without the domes.
One option would be to build the real armor out of
papiér maché -- or in English: paper and glue. That technique is often used to make the first prototype of a costume armor piece or helmet that is later cast, and in some circles very common for building the finished piece.
I suggest that you search this forum (and the web) for "pepakura", "Halo helmet" and "papier mache" and you will find a lot. The only materials you need are card, masking tape (because it is made of paper), paper, wallpaper adhesive, Bondo (or other Putty) and sandpaper.
If you do choose HiPS (high-impact polystyrene) plastic, then there is a "ghetto" technique that I practice in the kitchen, that I can share with you:
First, cut your armor
roughly to your template: Leave the fine trimming for when after it is shaped.
The trick is to heat the plastic just a bit and then hold it bent in a specific shape as it cools. The plastic will snap back a bit when you release your grip, but if it was hot enough to begin with then it will not snap back to its original shape. You need to bend it more than the angle that you wish to get.
I most often use an oven, set at the plastic's melting point. This is often just above 100 degrees C (melting point of water). Place a piece of wood inside the oven -- the plastic will melt if it touches the metal inside the oven. (The piece of wood can also act as a tray)
I put the piece inside the oven for 20 seconds, take it out, bend it and hold it until it is cooled. Then I do the same thing over and over again until I get the shape I want. If it did not bend at all, then I let the piece sit inside the oven for five seconds longer the next time.
Don't worry about burning yourself. You are not supposed to get the plastic
that hot, just
almost that hot.
It is imperative that you not leave it in the oven for too long. You do not want the plastic to reach its melting point because then it will become soft as butter, deform under its own weight and your piece is ruined.
Other people use heat guns, but this is how I do it. I find this method better for larger pieces.
There are those who warn about styrene fumes but I don't find them very irritating.
Either method you choose: Good luck, and remember to post your results in the forum!