One of the neatest tricks I've heard on here! Now I want to try it out.

 

Replaced mine with a 9" stubby. Radio reception is fine, even 100 miles away from the transmitter.
The only issue I have with the stubby is that it bends in the carwash, so I have to take it off if I go through the car wash. Talked to the vendor of the stubby and he said all of them were that way.
The antenna straightens out if you bend it back, but really how many times do I want to do that. I had the same issue as the op, the antenna scraping against the garage door. Never thought of chopping the factory one shorter.

 

I know this is an old thread but...
After trying to remove the ball with vise and vise grips and hammer etc. I was having no luck. Then I thought about it and realized the antenna looked to be about the same size as a pop rivet. I cut the top couple inches off with bolt cutter and sure enough it chucked into the rivet gun. A little squeeze and it came right off. No worrying about it shooting across the room or under the work bench. Clipped the wire, filed the coating off the end, put on a dab of epoxy and put the ball back on with a couple hammer taps. Since I marred up the ball with my failed attempts on the vise it will need a shot of spray paint.
M.R.
2010 F150 XLT