Thanks for separately and independently verifying the behavior of CDK09, at least I am not going crazy or my keyboard is not necessarily broken. Looks like it is to remap the combination I want using something like HotKey, this is so stupid.
After posting I also found to delete a word, you can use CTRL + DEL or CTRL + BACKSPACE, which does work on CDK09 and handles deletion of 1 word at a time – something close to what I do with CTRL + SHIFT + LEFT/RIGHT, followed by a DEL key. Maybe I use this combination instead and have to unlearn my familiar key strokes.