You are getting the same problem i had on my first try, you have forgot nothing, the Cap ends don't seem to work from a curve that was projected.

I extruded my before then use the tire profile to cut the un-wanted pieces and move the pieces a little higher with the move function to get the thread height.

That is a Test render with half of my tire



If i can i will post what i did later this weekend.

Thanks Micheal.