Michael,
(MoI is the greatest thing since sliced bread, I'll enjoy my remaining trial days and put it on my Christmas list)

There must be some way to at least introduce a simple command, even an addition to the Align tool set.
One that would apply tangential alignment to the edges and intersections of selected associated mesh networks.

I'm guessing that the first control points on either side of a network edge point would be averaged and moved to line up with each other through that edge point.
In operation, it would take no more time and effort than the process of Joining the mesh edges when you're done with them.

Even though, you'd still have issues with curvature continuity, you'd be providing a way to remedy those awful creases and lumps right at the seams.
These show up and gives a solid that unwanted "panel-ized" appearance. It's been the only disconcerting thing to me I've run into learning how to use MoI.

Maybe some type of averaging of point positions could smooth out those control points along the mesh, outward from the target edge.