the water depends on the amount of eggs, I dont know how big your bator is or how many eggs are in it. But if you have a bator that will hold 60 eggs and you have 6 in it then there is a lot of space only being occupied by warm air which will escape faster. Think of it like having a cold glass that comes out of the freezer filled with cold air, the cold air in the glass would probably only last a few second before it is mixed with warm air and replaced or warmed. If you took an ice cube out it would solid and last in its cold solid form much longer then the cold air in the glass. SO if you have a lot of space (air) in the bator the air will escape when opened. BUT if you fill some of that air with warm water in bottles then the temp would stay more constain since the warm water will stay much warmer for longer then the warm air.
As for the egg carton method, you can load all the eggs in cartons (large end up) instead of turning them you elavate one end of the carton in place of each turn. So say for instance you are currently turning at 7 am, noon, 3 PM, 8PM and midnight. You would put a block maybe an inch or so on one end of the carton at 7, then move it to the other end at noon, back to the first side at 3 etc.
(I really hope this makes sense)