We cannot offer medical advice, and frankly, we are folks whose experience is with insulin treatment of type 1 diabetes instead of type 2 diabetes (which is your condition since you are not taking insulin). However, the common sense answer is that if you only take one tablet per day, you certainly want it doing most of its work while you are awake and eating fairly often than at night while you are not. Even if you eat at 10:30 at night, your meal is pretty much digested in about 2-3 hours usually, leaving another 5 hours or so of medication not having any food to work off of. This would leave you at risk of lows while you sleep if you took it at night and its greatest work was done was while you slept. Better to have it petering out slightly in the morning and causing the slightly higher readings in the mornings than risking severe lows at night.
The nibbling is a good solution to meals for type 2 diabetics, for the constant flow of small amounts of foods keep you from having high readings after large meals. As for taking the test 2 hours after a meal, I would suspect that whatever your reading is at that time is pretty much your reading two hours after each of your snacks. So the information is still valuable to your physician.
If you are concerned about the slightly higher readings in the morning, I encourage you to discuss this with your doctor. He will probably want to see what your hemoglobin a1c is, and if it is slightly higher than what he is looking for, he may decide to alter your medications slightly, perhaps adding a tiny bit of medication at night. But if your hemoglobin a1c is where he wants it, then I would not worry over the higher morning reading. Your usual glucose numbers are pretty much perfect other than that morning reading, which still isn't awful. Your doctor can tell you if this is dangerous for you after he sees what your average glucose is by finding out your a1c number.
I agree with SGG that your overall blood sugar control is terrific. It's great that you do the "nibbling" thru the day. Many folks seem to experience, as you do, that their bodies can handle several smaller meals better than just a few large ones.
You mention that you're dissatisfied with your morning numbers. Many diabetics experience higher numbers in the morning from something called "Dawn Phenomenon." There is also a less common Somogyi effect.
You can read about these phenomena at (note that the website label may span 2 lines and you may need to copy/paste the whole thing into your browser):
You might compare your experiences & patterns with the info in this article and discuss them with your doctor. I have also read about different meds for types 2s: some give a long-acting, constant, steady impact and others are short-acting and help cover larger meals. I know that exercise can be a challenge to fit into your schedule, and yet some exercise in the evening might be a help to you. Gotta clear it with your doc if "starting exercise" is something new to you, of course.
Since your morning BGs are weighing on your mind, it seems like it's a really good time to discuss all the issues with your doc (do you hear a pattern of advice? ;-) ). You've become aware of patterns and your doc can help you interpret them. As SGG points out, your doc may simply give you a hearty CONGRATS! and encourage you to keep doing what you're doing. Hearing that from your doc can go a long way to quieting your concerns.