I have a great solution for installing a crown race with just plain PVC pipe, but am really flummoxed as to how to remove a crown race from carbon forks without purchasing a specialized tool or driving 30 miles to my closest bike shop? Any DIYers out there that have found a consistently workable solution? One that does not involve flat-blade screwdrivers...
There is a relatively cheap kind of crown-race removal tool that acts as a set of wedges that clamp down on opposite sides of the race to drive it away from the crown. It's very similar to a generic bearing splitter. So yes, it's a specialized tool, but not a crazy-expensive one, especially considering you could ruin your fork if you did it wrong.
There's another type of tool that looks like an oversized tuning fork, where you invert the fork, remove the wheel, and set the "blades" of the tuning fork on (what is normally) the underside of the crown race, and tap it in the center, in line with the steerer tube. This would be fairly easy to improvise using wood if you're handy. Caveat: I haven't tried this, I'm just spitballing.
A method I've never loved but have used a time or two and seen others use a lot is an old disembodied pocket knife blade and a hammer. Carefully tap it in along the spine at multiple spots to wedge off the crown race. This method does work well, including on forks that offer zero overhang of the crown, but it has some risk of cosmetic damage in the best case, and on a carbon crown I'd worry it might be capable of doing more. You could mitigate that risk by using a thinner blade, probably.
I kind of hate the idea of using this approach on an all-carbon fork (as opposed to an aluminum crown), but the truth is that proper tools work on a pretty similar principle in these days of zero crown overhang being common, and themselves are not totally free of any risk of damage even if used carefully, so it may not be as stupid as it seems. On an aluminum crown you can do it all day as long as you don't care if it looks pristine.
Here are a couple of suggestions, but as you are dealing with carbon not sure I recommend them.
Box knife blades - stacked together so you get the shape bit under the crown race and can walk it up.
Heat - with carbon use extreme care. Rather than a heat gun, a hair dryer and bring it up to a temperature no hotter than you can still touch. The crown race will expand and loosen.