I would love to have a discussion on the counting of carbs and the flexibility of changing the insulin units accordingly.
What's your diet/regime like at the moment? Are you on fixed amounts of carbs per meal? At fixed times? I'm a little puzzled in that you don't seem to be taking fast acting insulin first thing in the morning, as many of us need extra insulin then as our blood sugars go up because our livers pump out sugar to aid in the getting up process.
As a T1 on a basal (eg lantus) bolus (fast acting insulin eg novorapid) regime, my basal is meant to carry me through the day and night when I don't eat and then my bolus counteracts any meals and sometimes acts as a correction dose. (eg I gave myself 4 units of my bolus at 5 am this morning when I could see my blood sugar rising with dawn phenomena, and then went back to sleep. Not recommended to do unless you know this agrees with your body and its reaction to insulin, because you don't want to go hypo when asleep.)
My (very limited) understanding of T2s and insulin is that insulin resistance is a massive issue. Plus you may not know whether you are still producing much insulin of your own? But .if you want to go on a basal/bolus regime I would suggest that you talk to your diabetic team. I was on fixed doses throughout my T1 childhood (pre glucometer so it was pretty well all guesswork apart from the odd urine test) and found it very liberating when I moved to a basal/bolus regime in my twenties (and got my first glucometer).
As a child I rapidly memorised lists of carb values of proprietary food, now I go by a lot of experience and guesswork, though I still get out my kitchen scales occasionally. Modern prepared food in supermarkets tends to have carb values on it which makes things must easier.
So, in theory, once your basal dose is right, you need an insulin ratio from your diabetic team to calculate your bolus for meals/snacks. Typically they start at 1 unit for 10g of carbs, but it's likely that if you're insulin resistant you'll need more than that (eg I need 1 unit for 3g of carbs as I'm a bit insulin resistant thanks to the genes from my T2 dad). If your ratio is 1 unit for X g you just divide the total carbs for your meal by X to get the needed insulin. (Then add in a correction dose if your before meal blood sugar is too high.) But the whole point of the basal/bolus regime is that you should be able to have the meals when you like (including skipping them or having a midnight snack).
Having said all that, not entirely sure on the effect that your other medication has on the whole thing.
Hopefully you'll get some more responses soon. Good luck.