Out of the chicks I got from the above crossings, I've taken the best cockerel from one group and plan to cross him with the pullets from the other group.
Is this crossing procedure too closely related?
I don't think so and it sounds like a good plan.
My personal opinion is to start with the best quality stock of the variety you want from one source. Then develop two or more (more is better) breeding groups (stains/lines) from them, crossing cockerels from one group over the hens/pullets in the other as you said. Close breeding without breeding siblings or parents with offspring, after that first year, is my suggestion.
My concern would be crossing birds, of the same variety, from different breeders/sources. Generally it won't be a problem, but not every strain of a variety is necessarily built on the same e-locus genes or made up of the same genes from there on up. Outcrosses of birds from two show quality lines may reveal some traits that neither displayed. This is more apt to happen with some varieties than others.