I finally figured out how to get the Ninja (Style 1) suit after checking the reddit and doing my own experimenting. Go all the way to the side with the stable bumper (1 side rotates, and which one it is seems to flip occasionally). Drop your Mii so that it lands flat on the little angled projection right beneath it - basically let it swing all the way away from the side you're on, then swing back a little bit. If it lands flat on that first projection, you have a strong chance of ending up on the suit.
Took me about 20 tries for the first suit. Then I decided to get the white one as well, and got it on my first try after I realized that the left side bumper was spinning now, so I needed to switch to the right side.
Wish I could remember how I got the sword; I don't remember having any problem with it.