To remove a crown race, I usually start by tapping in a utility knife blade with a hammer, then get larger and larger (non-serrated old butter knife, then flathead screwdriver). That seems to do a good job without making much of a mess.
Like this:
https://www.youtube.com/watch?v=LnBC5CEdgi8
To re-install, I used to tap it on with a flathead screwdriver, but having a section of scrap PVC pipe I can use to tap on the crown race has made my life a lot easier.
You will also need to install a star nut, which is easier with the right tools. But I've also bodged it using a socket, like this:
https://www.youtube.com/watch?v=p2web0rlrX8