The BB is not too big.
Powerbites have a 22mm axle. The bearings say 22 on them, meaning they are 22mm.
There are a few sizes of BB. I will run you through them.
19mm. Usually solid axle cranks. 8 spline and more high end 48 spline. These are being phased out now, because to make them hollow makes them too weak for street riding, and thus the axle is forking heavy. Even in cro mo. TI axles are not great for 19mm because of the tiny splines.
22mm. A few companies used this BITD. Primo was one, but it was mainly FSA. It wasn't common then, but it is gaining a bigger following now. Mostly because with the larger axle you can make it hollow (and thus much lighter) without compromising strength. Most are 48 spline again, and not like Primo. Primo did a "hollow bite" axle like yours but it was hollow and much lighter. I call it the V2, many others don't and prefer to call it by name.
24mm. Which actually isn't 24mm. It is 23.8, the same as many sprockets come in (you don't need a top hat at all). Best and most popular now, as they are always hollow and really light and strong.
IDK why you are saying the BB is too big. Do you mean because it is too wide? do you have spacers? from what you are showing me the bearings are not on the seat. What I mean is, the seat of the axle is the round central part. Not those squared looking ends. Those are smaller than 22mm, and will move around. You need the central axle in the bearings. Not those squared parts. Depending on the width of the BB? you will need spacers.
