Yeah, don't use the tool.
Take the caps off (keeping them side to side and up and down correctly!), then you can put a wrench on one of the ring bolts (box end, I believe either 5/8" or 11/16"?). Now, rotate the carrier up until the wrench hits the case and won't allow any more movement. Grab a big screwdriver/prybar and pry on the teeth (since you're not reusing the gears) outward, keeping the wrench up against the case, still on the bolt head. You'll pry that carrier right out of there.
Since you're having to swap in the carrier anyway (especially since you're regearing and there is a carrier split) then you can just huck the thing! Keep in mind that next to each carrier bearing there is a shim. You'll need to keep them on their respective sides as well. It'll give you a place to start when seting up backlash and gear pattern.