Personally, I would wait until they are 2 years old and can use Camp Carnival.
Carnival is VERY strict on that age....23 months and 3 weeks won't even do it. They must be 24 months or older.
Every 3rd and 4th person in a cabin pays a reduced rate (regardless of age). But it is my understanding (unless something has changed) that Carnival does not charge tips for passengers under the age of two. So that is $20 a day that you would not be paying....
At this age, the only time you would not have the children with you is if you decide to take advantage of their babysitting service (which is IN Camp Carnival, not your cabin) from 10PM - 3AM.
Since you describe the efforts needed for the twins on a daily basis as being so tremendous...I personally do not think you would get your money's worth at this time.
I would wait until they are at least two years old and then you can enjoy some alone time....