From there, you have to work the safety out from the left side of pistol by carefully (and somewhat forcefully) vibrating and pulling the safety.
You'll see if it is in the right position because when you pull a bit, it will flex out from the frame. If it is in the wrong position, it really won't give. On pretty new pistols, this can be tedious - especially if you don't have a good set of small wedges handy.
I found that once you can separate the safety from the frame a few millimeters, you can slide a small zip tie under the safety and then zip it part way to create a handle. You can also put one under the front of the safety and, combined, you have a good tool to pull with that won't scratch the frame. You still have to jiggle and pull a little bit to get it to a point where you can separate it the rest of the way by hand.
Once you remove the safety lever from the left side of the pistol, the safety on the right side will rotate around to the top of the pistol. You can see some photos on this thread of this part of the removal.
Now you're ready to attach your new safety and reinsert the safety from the left side of the pistol. Reassemble your pistol and you're ready to go!
It worked like a charm and saved the cost of having to go purchase wedges and you'll reduce the changes of scratching your frame or safety. I hope this might help anyone in the future looking to remove the ambi safety. I didn't take photos during the removal process on this pistol but next time we do one, I'll take photos and add them to this post.