Well barnyard mutts would t be vaccinated unless you did it yourself.Good points. Cackle raises their own line of Buckeyes, and they are a huge hatchery so have big flocks. Does that help, or would theirs still be too inbred?
How do you order "barnyard mutts" - and have them vaccinated? Your Azurs are Blue Azurs, also called Sapphire Blues?
I know at Hoovers they have many different hybrids on offer - I got Midnight Majesty Marans which are BCM Roo crossed on barred rock hens. My one surviving chick turned out to be a boy

The Azur Blue I have are a Leghorn and Auracana cross hybrid. They look very much like leghorns, but are actually paint or splash in colour as they have black spots. And Topsy has a crest!
There are so many nice crosses out there these days. Have you seen the Welbar cross Hoovers has? Welsummer and Barred Rock cross.
I would actually buy the Azur again they are super friendly and funny little birds - I was very happy at how friendly they are considering they were ‘factory’ Ready to Lay pullets when I got them at 20 weeks.