On testing and weighing, I think it's a combination of what you're measuring, and consistency. So if you test BG first thing on waking, result will be influenced by the liver dump/dawn phenomenon. Pre/post meal would give you an idea of how you're responding to that meal.
For OMAD, I'm not sure whether time of day matters as much. There may be some differences based on exertion profiles and possibly natural circadian rythms, but it'd still be one meal a day. And if lunch is more convenient for your family, it's going to be easier for you to stick with it.
And.. don't sweat the small stuff! I'd suggest keeping a note of your results so you can graph them and look at the trends. I think there can also be a danger of getting obsessed about daily readings and changes and possibly trying to correct for those. If you just carry on LCHF and/or OMAD and the results after a month, 3 months, 6 months are showing you a nice trend, that's all good!