Apparently Range mode does have a significant impact on the battery balancing. Either that or 110V somehow squeezes more in.
I think that both things are true.
I recently took my car in for its 24,000 mile service. Apparently, there was a problem with some $.01 rivets in the sheet metal of my battery, and so they had to replace it. I got a battery with about 6000 miles on it (a big win for me). The Tesla service guy told me that the new battery was horribly out of balance that I should charge it all the way up in Range mode and then let it sit there. Not overnight, but for lots of days. I was surprised about that, but I did it anyway.
When I first got the new battery, it was charging to the low 170s in standard mode (and I think around 220 in range mode). After doing several range mode charges and letting it sit, the standard mode charge crept up to the low 180s. Then, over the next month or so (without more range mode charging) it's now getting 185 or 186.
As I understand it, the issue with battery balancing is this: There are a number of sheets in the battery. During charge and discharge, they all run in parallel. However, due to whatever reason some of them can wind up with a smaller or larger charge than the others. When you're charging, they all get the same amount of energy, and the charge stops when the most full sheet hits its charge limit. However, as you drive the car you need to stop discharging when the least full sheet hits its low charge limit. Therefore, you've effectively lost the part of the battery that's between the two.
Let me give an example. Say that one of the sheets has 10% more charge than the others. When you charge up, you stop when the extra-full sheet hits its limit (say 85% state of charge (SOC)). When that happens, the other 10 sheets are only at 75% SOC. Then, when you run the car, you have to stop when the less-charged sheets hit the lower limit (10% SOC or so). As a result, you only get to run the battery from 75%-5%, or 70% of the total capacity, as opposed to running it from 85%-5% and getting 80% of SOC as designed.
Balancing will even out the charge in the sheets (either by lowering the overfull one, increasing the others or most likely both by moving charge between them). The result of this is that you'll be able to get all 11 sheets to 85% charge and then down to 5%, and it will look like your battery has added capacity.
What's interesting (and to me unexpected) about this is:
1) It's remarkably slow. This takes DAYS (or even a week) not minutes or hours.
2) It works much better in range mode than standard mode
So, never charging in range mode may well be reducing your effective battery capacity. The good news is that you can fix it by holding your nose and letting it charge and sit in range mode for a long time.
Tesla service can tell you if your battery is out of balance.