Sorry, the progressive style hook is the peterson reach tool.
I'm not sure what you are referring to. Are you referring to the pick at the bottom of each picture which has been included for comparison?
The others however were designed by Barry and his team.
The style is basically the same as the Falle. I don't think Barry and his team performed "clean room design". I think they would have been exposed to the Falle Set before they designed the HOPE Set. The influence is clear.
You can find similar hooks in petersons DCAP set, but some hooks are Barry's own design.
A curved pick is a curved pick is a curved pick...
This I know for a fact. I own all sets, Petersons, falles, hope 6 sets too. They are all different.

I own the Falle Set and most of the Petersons. I agree that the Falle's are different from the Petersons but the HOPE Set have the same handles as the Falle's (except for the slots) and they either have a curve or finger. They look the same to me: an arc (of the same degree) is an arc (of the same dgree), a probe is a probe and a right angle is a right angle.
How specifically are the Falle's different from the HOPE Set?