Rest the card on a thick book (or even two) when you draw the outline before cutting around it. That will compensate for the cone of light that centres on your enlarging lens. If you draw it on the baseboard, it won't natch when you hold it above the paper at the right height for dodging.
This is what I do. If you burn with your card closer to the lens you'll have a softer outline cast on the paper so it won't be as noticeable. Make sure you move it around alot so you get an average sort of exposure over the transition area. It doesn't hurt, when you are burning, to expose some more of the rocks when you move the card around, in fact it makes the halo much less noticeable and provides a cleaner transition.
The problem with burning and dodging is repeatability. The masking method is of course repeatable, but takes time. I will throw one more method out there for you that is repeatable as well. If you have a diffusion enlarger and a glass neg. carrier you can do this. I tape the neg in the carrier then I tape a piece of frosted mylar on top of the carrier. Put it on a light table and with a pencil shade in the areas that you want to hold back. No muss no fuss and it works surprisingly well. Most importantly it is repeatable. Give it a shot.