Yakuake is a great Terminal. However, it is not obvious (probably), but it should have an option to be centered/aligned in relation to a specfic DISPLAY. This can be done (faked), by setting the Left/Right position in the options. The problem is that this method uses the whole Framebuffer size and not indivudual displays. The incovenience arises, for example, in a notebook that has different display configurations at different locations. The worst thing that can happen to a Terminal application is to be divided between 2 displays of different sizes. Reproducible: Always
So the option to open at a specific display does not work for you?