spare tire carrier doesn't handle 15"

[argheebe]

I upgraded 3 each 14" 215/75R14 to 3 each 225/75R15. No problems with the wheel well fit in my 2006 2720SD with a 2 1/2" lift kit. The tires were Carlisle brand, load range E. I feel good now after having a driver-side blowout going up Vail Pass on I-70 recently (snowing at the time).
I wonder if anyone could offer a suggestion about how to mount the 15" wheel/tire combo in the same place as the 14".
The two holding studs that are presently in place are just long enough to poke through the 14" wheel-with-tire and able to snug it down with the provided wing nuts.
The 15" wheel-with-tire is just tall enough (sitting in the carrier) that the studs are about 1/2" out of reach. Drat!
My thoughts are to get a female/female threaded stud extension (assuming it will fit through the stud holes after being attached to the original studs) and then use the provided wing nuts.
Of course, my ideas are limited and so I am asking for suggestions.
I did a search and was unable to find anything on the subject.
Thanks to all of you out here on the forum. ....a great help in so many ways.
Ron