I strongly suggest you not syringe the food into either cat.

That will create stress and fear and dislike at food time.

When introducing a new cat to a family home, food is paramount to create safety for both that neither will go without. Place the food dishes farther apart and they will be less competitive. Usually one cat will become alpha and eat first, then leave and the other will come later for his/her share. Some cats we have had do revenge eating... that is eating both dishes in fear that the other cat will get "more".

We use treats to reward desirable behavior. Each cat must have a favorite...it has been our experience. Our Maya gets a defrosted cooked shrimp when she is behaving well. Weezie will get cut up left over chicken. They both like Chicken of the sea Salmon (from the pouches in the human food aisle).

When both of your kitties learn that the food is plentiful and given on time, most of the tension about the new Misu will dissolve away. Try not display tension or worry over looking at the food dishes. They won't understand those feelings and think THEY are at fault somehow.

From what I"ve read so far, your new kitty sounds nice and socialized. So you should have a good life with her with little stress.

In our home Weezie mostly defers to Maya. They get along very well since neither really want to be alpha. But we have had others that established a pecking order..it just depends on the temperaments of each cat. Weezie does want to be higher up in the cat trees though.. that remains a slight bone of contention even now.