Quite frankly you do sound like you are being unreasonable and making your children pawns in your ongoing battle for control which I susspect was an issue in your marriage. You also sound like you are trying to get more time for the sake of getting more time, also it has changed for both of you being in new live in relationships, now you admit she is remarried, might that have something to do with your intent? IN your letters you SHOUT BY USING ALL BOLD TYPE!!!!!!!!
TRY USING "I" messages rather than accusing her. It is not reasonible to expect children to always go to bed so early, so being up late on a Sunday night is not unusual, most likely they would still be up that late by the time you got them home if you picked them up at 7:45, I'll bet you interrogate them. Let them have peace, if they want to call let it be up to the children, not a forced visitation. You are using these as excuses to get control and everyone sees straight through you, is it any wonder your ex is insisting on keeping to the agreement.
You achieve what is in the children's best interest by relaxing some. Several people made suggestions that allow both parents equal time, that is not what you, want but that is what is fair and good for the children. All this stress isn't good for anyone or any of the relationships.
My suggestion is since your ex has Friday's off and I assume you do also as you stated you worked 12/3/4 schedule that you do also, so a once weekly exchange on Thursday evenings, allows both parents an opportunity for extended weekends (3 day) with the children for trips and the other parent a totally free week and weekend, alternating every other week. Allowing for some negotion for vacations if you can manage that. That doesn't mean that you can't help at school or be there for special occasions, but being reasonable. Then the children get to sleep in as long as possible where ever they are on school days and later during school vacations. The routine will do them good and it will do you good too to have some weeks with less "interrupted sleep". I used to work graveyard, then do my internships during the day, so I know what is happening with you getting interrupted sleep, your mood may improve with this new schedule. I don't know how far they live from school, is it possible for them to walk to school or take the bus? Day care is not the worst thing that can happen to a child better than all this stirfe. Think about these things.