Why can't your lawyer enlist the services of a father's rights advocacy group? I'm sure that you are paying her top dollar for her services, seems like something SHE would be on top of, particularly if custody time is primary concern in the settlement agreement.
Is it possible that with a 50/50 arrangement your child support would be reduced enough to afford a nanny for those nights you are on call? I'm sure it's expensive, but as others have chimed in already, once this agreement is made, you'll catch hell trying to get it changed in the future. As far as that goes, what are the possibilities of a change in your schedule that would reduce the amount of overnight on-call responsibility you carry?
I think it's long past time to start playing rough legally with your wife. In your shoes I am inclined to think that I would tell my attorney to pull out all stops to make a proper agreement happen.
Blessings,
Bill
"Don't tell me the sky is the limit when there are footprints on the moon."