Deep breath, hold, release, deep breath, hold, release. Repeat as needed.
This whole 'sugardance' takes time. You've already started to do some good things for your kitty Pepper, like feeding her low carb canned food. This sugardance is a marathon, not a sprint. It takes time and 3 weeks is actually very little time for a newly diagnosed kitty.
I bet you see some other positive signs in Pepper, even if the BG numbers still look too high. Peeing less? Playing more? Purring lots? Appetite good? Pooping normal? Drinking less water?
You could try giving the Novolin (NPH type) insulin every 8 hours, schedule permitting. Not always possible but worth a mention.
If, and it's a big if, you decide to ask your vet about trying Lantus insulin, get a prescription from your vet and order the insulin from Canada. Lots of folks here have used Marks Marine Pharmacy for the insulin. Canadian cost for lantus is a fraction of the cost that it is here in the US.
What is your favorite color? I'll loan you a pair of my 'patience pants' if you like.
p.s. My cat Wink was on Humulin N initially when he was at the cat shelter. Switched to Lantus by the vet and unfortunately high carb Hill's W/d dry cat food. At least you are feeding better food to Pepper.