This is a great question, thanks. One of the things to keep is that the current weld function only works on open boundaries. Other packages will collapse unneeded faces, which is a great option we will look into.
In this case if you removed the triangles that won’t be needed first with triEdit.
then while still in triEdit use the edge weld option.(the first selected edge is the edge that will shift)
You should get the shape you were looking for.
-Russell