If the crown race is a really tight fit, you can do a few things:

Use heat/cold - chill the fork (if you can fit it into a freezer) and heat the race - 200F won't damage anything, and see if the hot race will go easier onto the cold fork. Be quick - the race won't stay hot for long.

Use some emery cloth or a rolled up sheet of sandpaper to increase the interior diameter of the race (I personally wouldn't attempt to sand the fork, but others may differ here). This will likely be a slow process.

If the "race" is merely the support for the actual bearing (i.e., the bearing is a self-contained unit - the actual terminology escapes me), then use a Dremel or saw to cut a slot in the race. It's go right on and still do its job of supporting the bearing.
However, you go about it, I wouldn't be too concerned about scuffing up the surface of the carbon, as long as you're not digging into fibers themselves

When I installed a King race on a carbon fork recently, I used a metal tube of suitable width (the handle extension of a floor jack, IIRC) which fit over the steerer, and a white PVC pipe slip coupler, which slid over the pipe, but which contained an inner lip to prevent the pipe from pushing all the way through. The coupler was the right diameter to sit on the race, and the plastic was less likely to mar the race during installation. I rounded off the edge of a short piece of 2x6, so that the rounded edge conformed well with the "crotch" of the fork, placed the 2x6 between two trestles and sat the fork down onto the 2x6. Dropped the race on, slid the pipe/coupler over the steerer and a few robust "taps" with a lump hammer later, the race was firmly set.
The coupler is now irreversibly jammed onto the end of the jack handle, but I how have a "go-to" crown race installer