Rightclick, break is the option you are looking for. Select the edges and break em, then move the islands apart And you shouldnt need to move points closer, just raise the weld treshold. If yiu set it to 1 you should be able to weld everything in the 0-1 range into one clump :)
Take another look of what i am doing. It will always weld verts first that are connected in the model and closer to each ither. There is a reason i go down the seam one by one :) If you feel like thats too many points, move them close to each other closer than the actual connected geometry is and play with the weld value.…