I only own a couple of very early (late 20s early 30s) Kaywoodies and neither have the slightest problems.I think you’ve got that backwards. The early Syncrostem (1929) mortise assembly was threaded on the outside to mate to the shank. Long before Lee showed up.
In fact of the at least a hundred Kaywoodie pipes I once owned (and sold off all but the best 4 hole stinger versions) only a very, very few have pulled the mortise out, and none the stem like the OP.
Some of the later, varnished 3 hole stinger pipes had shallow threads on the mortise. Earlier versions that popped out seemed ribbed, as though pressed in place.
Just before WW2 American pipe makers churned out about 30 million pipes a year, and Kaywoodie bragged 11 million were theirs.
KB&B had a virtual monopoly on high grade briar, until Hitler’s U boats shut off supply.
Late thirties Super and Flame Grains used the best briar the world will ever see again. Kaywoodie showed X ray machines they utilized to scan 200-400 year old briar roots the size of big color console television sets.
Then the war forever ended the use of briar of this grade.






This is a large ball, Drinkless registration stamped 4 hole pre war not marked imported briar Flame Grain #13 Dublin..
Lee never equaled this pipe, but nobody else did either.




Be extra careful to keep an old Kaywoodie clean, and don’t abuse one.
If the mortise or tenon pulls out, it’s time to send it to Briarville.