The stopper actually was a combo glass top and stem stuck into a cork....so, no the neck wouldnt have been ground to match. Ours is a WT & Co as well. The stopper is stuck and I dont dare force it out.
Nice,one of the most valuble sizes,and the smallest i collect the WT lattices. Here is what the stopper looks like and yours took the smaller size of the 2 sizes.They did not come with stoppers they were optional.Nice digs.