I watched/helped Paul A do the broomstick trick on my conversion. He spear tossed the handle into the tunnel. It took a few tries as it's a timing thing, getting the U-joint to catch the stick at just the right time so that the stick was "trapped" as it went round and round beating the tunnel the out. Interesting thing to see, but seems easier to me than cutting and fabbing, especially if your carpet is already glued in. The most time consuming thing is putting the car on the 4 jackstands, but since you're already in the middle doing the conversion, that part is done already.
Another fix that may need done is because the shift stick doesn't come up in the center of the hole any longer. One method is to get the gaiter ring from a later car and use the leather gaiter instead of the (remove able) shifter can. I was lucky to know a guy who could weld. I had him cut 1" off the height of the can and fill in the hole. He then redrilled the hole effectively moving it forward. Got a rubber gaiter for an MGB and away I go.
YMMV
My 2¢