Help with replacing existing tree logs?

Unfourtanately, I don't think there's an easy way to do this- if it were a structure, you could just modify the structure file, but trees are biome features, and there's really no way to mess with existing ones. My advice would be to find some way to remove default azalea trees and replace them with fully custom ones. 

...Alternatively, a workaround you could do is make oak wood drop your custom wood block when mined near azalea leaves, but this would probably a bit broken. I guess if I were doing something like this, I would add custom Azalea trees that exclusively generate in the Lush caves themselves, incorporating a combination of Azalea and Oak wood; or adding smaller Azalea shrubs of that wood type. (Though getting underground features to work is a bit of a hassle too.)