I won't be able to give you much advice, since your A1c's are better than mine. Currently I am at 6.9%, the lowest it has been since 6.3% over a year ago.
It appears that you are doing well. That said; in answer to your questions:
"1. Is my thinking correct about my bs needing to be at least 140 or below before eating between the three meals?" We all need to try and keep out BS at an average of 140 or below. Personally, I wouldn't think about eating at ~140. At 70 it would be another story. I try to keep my BS in the 100-120 range between meals and between 70-99 fasting.
"2. And can many diabetics tolerate snacks between meals?" Most any person with diabetes can tolerate snacks between meals, but if you are Type 2 you may have to take a 20 minute walk (exercise) and if you are Type 1 you may need to take an insulin injection. Most people use snacks to offset lows and do not use it to get their meal plan in. One thing that can be said for your approach is that it keeps your metabolism at it peak potential. This is great is you are trying to loose weight.
Have you considered counting the carbs and taking a bolus insulin injection for just the carbs consumed during each meal?
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Regards;
Danny 
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