Bullet proof vests don't use just a handful of layers. I don't know how much your supplies would cost but 30+ layers of kevlar plus epoxy around a bell means material costs beyond $100 for me. So I think the trans blanket suggestion was a good one, unless you really want to get the experience.
If you worked for an exotic car mfr (front engine/trans) and they wanted something more classy than a blanket I think this is a really good idea. You could even take it to the firing range and put a small caliber bullet through it as a simulation. I wouldn't bother with the carbon fiber.
The vest that SAVED my life was a solid 3/4"carbon
fiber... the chopper crews wore them(most of the guys
sat on them... they were heavy and had just a front and
back with velcro straps to hold it on... I was hit in
the chest with part of a B-40 rocket... it blew me back
about 15' and I hit a guy behind me and I broke his nose..
a couple other parts got me.. one in the shoulder and one
in the side... but I walked away and still kept fighting
till I could be choppered out.. then the chopper was shot
down(about 60' up) but we all got out before they hit it
with a mortar round...C/F is STRONG stuff.... if I would
have had a normal vest on(the army style) I wouldnt be here
