Hi Tony,
A close-up of just the Statue of Liberty stamp would be helpful.
Second stamp has a "4-Bar" cancel on it, a device made of rubber and common to small and medium-sized offices.

Third stamp shows a portion a machine cancel from New York City's Church Street Station, resembling a slogan in overall format.

To paint with a broad brush, yes, precancels are generally intended to be used on small-sized stamps, but the precancel specialists can provide a more detailed answer of the postal rules and how they were bent. Sufficient to say, the vast majority you will find will be on small-sized stamps.
Two U.S. slogan cancel references come to mind:
Moe Luff's "United States Postal Slogan Cancel Catalog", 2nd Ed, 1975.
The Machine Cancel Society's "United States Slogan Cancellations, 1899-1940".
Both have the limitation of cutting off the modern material.
It may be easiest to post your images here.
(LOL, Stallzer and I were typing at the same time!)
Add:
The two slogan cancels illustrated in the first post are:


Both were used in many cities.