Thank you all for good and useful input!
We have now switched to piling up money in the bills account, and it feels pretty good. Easy, and satisfies my hoarding tendencies. Shouldn't take us more than a month or two to build up a month slush fund without moving anything from the emergency fund. After that, we can start moving the surplus to other savings accounts.
I'm used to getting paychecks almost every week, but from April we'll be getting paid only on the 12th and 20th....
If a slight change in when you get paid causes you to adjust your transfers, to me that's a sign you need to keep a bigger cushion in you checking account. Keeping your accounts tight like that to squeeze out a slightly higher return is like picking up nickels in front a steam roller. It will work fine, until it doesn't.
We do have a lot of safety mechanisms, so there really was never any risk. I'm horribly risk averse, and have a background in risk planning, so there is always a plan B, and C, and W, X, Y, etc.