Mike, this can be done with a little patience and trial. First, mix a few cups of drywall mud with a SMALL amount of water to dilute it; I'd start with 2 cups mud and a tablespoon of water. You may need to adjust this as you go; more water=softer pattern, less water=heavier pattern.
Then, on a scrap of drywall or other flat material, try applying the mud with a paint brush, hand whisk broom, wallpaper paste brush; anything you think might give the right look. Play around with this until you feel you've got the method down, then put it on your ceiling. Overlap your new work onto the existing ceiling around the edges, and step back to look at it every now and then. If part of it doesn't look right, simply use a damp sponge to remove it while its wet. You can also do this after it has dried, but wet your sponge a little more, and give the mud time to absorb some water before trying to wipe it off.