With chicken eggs I've never used uber fresh ones... not same day... but same week, yes. And I've noticed the firm white thing. Kinda rubbery actually. But still tastey. Agree with the others you might try some two week old ones, a small batch, to see if that helps?? Throw in the milk for thinning the yolk too? May be worth a shot. We LOVE Deviled Eggs around here... chicken anyways... and hope one day to have ducks so I'm curious as a cat about this.
Oh... and I'm weird about cooking them too... I've tried a LOT of methods but lately I've been sticking to bringing them to a boil, then turning off the heat and covering and leaving them alone for 20-30 mins (may need longer for bigger eggs) and then tossing them into iced water for 10 minutes... peeling is SO much easier AND bonus points for not having green (burned) yolks... just my method, not perfect by any means... but we like it.