In the infirmary, you don't need to heal all troops at once. Adjust down the sliders and you will heal fewer troops.
Why do that? Well, once a heal is underway you can request help from allies to speed that healing session.
By batching up heal sessions into groups that can be fully helped by allies, you can instantly heal any amount of troops.
Go to your Embassy and click on Details and look for Ally Assists and Ally Help Time. This is how much help you can get for each request.
The black numbers are your base levels and the green numbers are additions from research. You need to add the two together.
Fill in the yellow boxes ↓ below ↓ with your personal stats
Make sure that you adjust the infirmary sliders such that the number (in time) of heals you submit is not bigger than this immediate help number & revel in the power of instant healing ... or shout at your team-mates to assist!