Hi and welcome to the forum.
Well done starting the test the blood glucose numbers. It will get much easier as you and your kitty settle in to it!
As mentioned above as the prescription food is very high carb, do not switch over until you are able to test during the cycle. And do it gradually over a few days as the change in food could drop the blood glucose more than 100 points. So adjusting the insulin will be important. When you decide to do it, come online and someone can help you through it.
Were ketones mentioned at all when your kitty was diagnosed?
If I were you I would get a bottle of Ketostix the next time you are at Walmart or a pharmacy. You just need to collect a urine specimen from kitty and dip the test strip into the urine then read the result exactly 15 seconds later in a good light. Anything above a trace needs vet attention. The reason we like to test unregulated diabetic cats, especially new ones, for ketones is because they can be more prone to getting ketones which can lead to the dangerous ketoacidosis (DKA). This can be avoided just by testing for the ketones.
If you could set up your signature (that is the small writing below everyone's thread) that tells us about you and your kitty and then we don't have to keep asking you the same questions over and over again. People who help you will always look at the signature and the spreadsheet before offering help. Make sure you mention what type of glucose meter you are using....human meter or pet meter thanks.
Are you feeding during the cycle, not just at the time of the injection? We recommend giving several smaller meals during the day and night. Most of us feed at shot time and two or three other times during each cycle, using during the first half of the cycle when the insulin is strongest.
You asked about giving the insulin 3 hours later than normal....the problem with that is it will completely throw out the shooting schedule. If you get a lower than normal number at shot time you can stall for 20 minutes, don't feed, then test again to see if the number is going up. For newly diagnosed cats we suggest you don't shoot numbers under 200 until you have some data on the glucose numbers.
Here is a link for new members you might find useful
http://www.felinediabetes.com/FDMB/threads/new-how-you-can-help-us-help-you.216680/#post-2450969
It is a big learning curve in the beginning and can be stressful but it does get a lot easier and you will soon be in a manageable routine. Keep asking lots of questions, we are very happy to help.