I dont think that you could be sure that introducing a pure breed would mean that they are not carrying anything. (Ask me how I know
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Re the mixing - Ex bats tend to quite eherm "assertive" in their dealings with other breeds and the saying birds of a feather flock together can be very true with chickens. So, If you want a nice quiet carry on with happy healthy, stress free hens I would either chose some attractive good laying hybrids such as bluebells or amber star or some large fowl that can hold their own with the ex bats such as sussex perhaps or blackrock for instance.
I would avoid any gentle, docile breeds or bantams so not, silkies, pekins, croad langshan, cochin, orpington as they are likely to get bullied despite their size.
And re the two coops idea ... you will probably find the majority opt for what they see as the best coop which will either be because its familiar, or because their is safety in numbers and everyone else seems to be in there. The ones that opt for the alternative will either be the most dominant, independent hen who doesn't want to slum it with the social climbers or the lowest ranking "cinderella" hens or a combination of both. You may also find the odd hen that decides to have a sleep over at the other place fro time to time.
You will probably find it easier to have one coop to maintain but the hens will probably prefer the option to swap around. If you invest in a modest coop for the introductory period ( which could take all summer) then you can always use it for quarantine, broody hens, poorly hens in the future or for those who really dont get on with everyone else.
HTH