That is exactly what they are though "intergrade" is more correct.
They are definitly not Brooks and here is why.
If you look at your snakes right off you can see that there is a wide space between bands. That translates into a low band count. True Brooks Kings are more than just a pale Florida king. The classic "patternless" Brooks was the result of a very high (78-100 ) band count. Of course today with the new definition of Brooks as just being a "color phase" some could argue to the contrary, that only color matters, but I will stick with what I saw collected from the wild some thirty years ago.
There have been plenty of snakes taken from pale populations of Florida (intergrade)Kings (most notably) from near lake Okeechobee that have been sold and consequently bred under the mistaken idea that they were Brooks.
This kind of confusion is one of the problems some of us forsaw with the increasing scarcity of wild populations vs advancement of breeding and "hybridizing" for color and pattern.
Frank
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"The luxury of not getting involved departed with the last lifeboat Skipper..."