I am in the home repair business and I can patch any drywall hole, but, as I tell all my customers, it is very very difficult to re create as you say the original texturers work. Normally a patch will always show and will be conspicous.
Your ceiling pattern even makes the job harder. Here is what I would do if your still going to do it yourself.
You need a star pattern from a good star on the ceiling. I would apply the same color paint to one star. Do not apply it too thick just paint one complete star. Now, with a piece of contrasting manilla art paper press this paper up against the star for a print. the paint will dry and you will have a good copy to re create.
Now, when you have the hole patched, be careful to not trowel the mud over onto a good star. Make sure the hole is level. You know that most compounds shrink upon drying, this is why you apply multiple layers sanding between each one. When level and dry, you want to apply a smooth watered down layer of mud. On this area you will use tooth picks or an awl to re create the star from the copy that you have been practicing from.
Nothing about this project is fun or neat or something you will ever want to do again. But this is what I would do.
Others should have ideas also. I would be interested in seeing them also.