When you got your cat did they give you the vet records then? Or can your vet call their vet to work out what has been looked for so far...
I don't know that what is ok for most Savannahs is the answer here as most Savannahs don't seem to get itchy from food... and chances are your kitty is special in their needs. Generally with itching you rule out the simple things first like fleas...even if you don't see fleas it is worth treating, my husband had a domestic cat long ago that a flea had only to get within 10 yards of her and she'd be pulling her fur out. We had to be very very regular with flea meds year round to keep her happy.
When looking at food allergies, there are prescription diets which it sounds like she has had... but there are also commercially available ones at your pet store that work out cheaper... still not cheap as they have to be formulated excluding the common kibble ingredients that are generally used because they are cheaper! I know Natural Balance makes a few "limited ingredient" varieties like duck and pea or venison and pea in both canned and kibble. For some reason although chicken is a common enough food allergy, duck is different enough. Fish can be a common culprit of food allergies it seems.
Read the labels at the pet store, just being labeled holistic doesn't mean it will be good for allergies, although generally means it is a higher quality food. Even organic doesn't mean it won't cause allergies. What you want to look for is a food that doesn't contain the commoner food allergy culprits: fish, chicken, corn, wheat.... the easiest thing to do would be to remove all and see how she goes. . Be aware it can take some weeks for a system to calm down from allergies though, so don't expect overnight improvement...
But overall, I would involve your vet in this as they can suggest things that might not be thought of here by being able to examine your cat (which we can't)...
