Covid can be awful. I hope the Paxlovid helps. I came down with it in late November and was fortunate that it was a mild case. The cats liked that I was home!
There are some aspects of treating diabetes that can seem illogical. On the one hand, you're correct -- food can raise blood glucose (BG) levels especially if the food is high in carbs. In a non-diabetic, when our cat eats, it stimulates the pancreas to release insulin. Insulin transports the end product of our metabolizing food (i.e., glucose) into the cells. If the pancreas isn't working, like in diabetes, the glucose floats around in the blood and doesn't move into the cells. We give an insulin injection in order to get the glucose to where it needs to be. As Daphne's numbers are improving and you're needing progressively less insulin, it's telling you her pancreas is beginning to work again. As a result, if you give her food, it stimulates her pancreas, the pancreas produces insulin, and it helps to pull her numbers down.
Since you're seeing lots of green numbers during the middle of the cycle, it may help to give a snack at around +8 or +9 and see if it helps to bring the pre-shot numbers a bit lower.
You may not need an elaborate feeder if you are around during the day. It may be helpful to have a simple feeder for a late in the cycle PM snack so you don't have to wake up.