100Wh is always allowed in 'user quantities', so 2 fat powerbanks in no issue.
Bigger is also allowed but (officially) you have to ask the carrier for permission. That's before you check-in your luggage.
Carry on is preferred but before I knew that I put about 5 18560 cell in my check-in without an issue.
About 2 months ago when they wanted to ban all laptops from carry-on the idea was that you checked them in.
With that they broke their own advise/rule. So my guess is that they don't really care much about the size.
I've seen 30,000 mAh powerbanks but they are quite rare. 26,800 is just a little below the 100wH limit.
If you need even more power you could take two. A little more expensive but also more flexible because you don't always need a big beast bank.
I usually fly with Delta, always the same route. They have USB power on every seat in a number of planes. I have no idea if it's possible to predict which flights.