Edge -- there are lots of ways to catch bullies, and I'm sure you can get lots of different advice. I looked through your links, and here are my thoughts.
I really like the single-lead trap nets. The Sterling website called them "Indiana trap net." In my opinion, there is no need to bother with the extra wings. If you set that trap net after ice-out and before the vegetation gets thick, you'll really catch the bullies.
It is a bother to set those trap nets; we usually do it from a flat-bottom boat. We stake one end on shore, often using a piece of re-bar to connect to shore. Then, you back out, feed out the lead, and drop the net so the frames will hold it square on the bottom. Because the trap nets are a little complicated, I wonder if you might find it easier to just use a 2-funnel hoop net. The "Texastastes" website had a photo of a simple trap, and you could set and pull it with chest waders. However, I didn't see any mention of twine diameter or strength at their site. Be sure that you get good quality twine, or the nets will not last long. It might be worth paying a little more to established companies such as Sterling or Nylon Net, and get some good gear.
I'm sure that bullies will go into smaller traps as well. They seem to like structure, and I'm sure that's what these nets and traps appear to be. However, I'll bet that the trap nets and hoops nets will catch more per effort.
Let's see if anyone else has other advice. There are many ways to accomplish your task. I just noted our common methods.