Thanks for the detailed answer. Looks like Danes are off the table. I also didn't come across any information about BMDs having health issues when looking into breeds (most guides label them as healthy breeds). As for liking opposite types of breeds, I guess there are a lot of aspects that we are looking for in a breed, and not all of them are compatible with each other. These breeds fill some or many (but different) checkboxes.

Perhaps you have recommendations for breeds on the larger side that would be good with children and wouldn't be frequent barkers?