When I first received my Ilium shift extender about a week ago I had the same experience as you when installing it. I subsequently took the shift arm plate off the bike, disconnected the shift linkage so the assembly was free, and went to the work bench. I braced the elbow of the shift arm on a block of wood and whacked the end of the Ilium piece with a plastic mallet. Now it's seated nicely. Perhaps more effort than necessary, but actually only took about 10 minutes.
There may have been a trick with WD-40 or something that I didn't think of or try, that would have made the initial installation easier.
I would use water and soap as opposed to an oil type of lubricant.
That worked great on the Grip Puppies!
You can also use a C-clamp to push the extender on the shifter.
When installed I would also strongly suggest "wrapping" up the extender with something soft as the metal thingie will do a number on your leather left boot.
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