Perhaps I was too hasty in my reply (again) so I've had a look at ways to increase infirmary capacity.
Knowledge - Training - Infirmary Capacity 50%
Inga the Wise - Infirmary Capacity I 80% II 150% III 200% - total 430%
Revival Rune - Infirmary Capacity 15%
Clan Stronghold Knowledge - Military - Infirmary Capacity 24%
Clan Stronghold Knowledge - Special - Infirmary Capacity II 100% III 200% - total 300%
Nothing from VIP or Aesir that I can see
So even if we leave out runes for the moment, 50 + 430 + 24 +300 gives 804% so looks like 2.2M might be possible with the 3 infirmaries 33,31,31.
What is curious about this for me is that you would want your infirmary capacity to be highest when you would lose many troops in defense but Inga the Wise is not the obvious choice in defense. This would be a situation where being able to use two shamans at once would be useful.