I would visit both schools to see how this actually works. Now you may know the formal school schedule but you don't know how it actually works.
The primary focus for M. when I assess schools is on the ambience of the school as long as the school has a good rating in academics. I want a school in which the general atmosphere is friendly and the needs of the individual student is a high priority within the school's structure. I want a school with a supportive environment. If they have supports in place the lunch time will work for most students and for those it doesn't work the school will help figure out how to help my child cope.
Spend time at the home school first if you'd prefer a shorter commute time. Feel the overall energy. Is it positive? Meet staff to see how they interact with student's and parents. I suggest that knowing the principal is important because they set the overall tenor for the school. Write a list of questions based on your concerns.
As a past volunteer playground supervisor I saw how the staff worked together. I don't remember specific times for lunch/playground times but I do know that if the times they set weren't working they would change them. My granddaughter had some special needs and her teachers and school counselor found a way to help her. The same happened with my daughter.
I suggest you really don't know how well the school will meet your and your child's needs until you spend time at that school. When my daughter moved she could've transfered her daughter to a closer school. She chose not to because of her satisfaction with the current school. My granddaughter could catch the bus for either school.
In our school district a child is required to be enrolled in the home school before the parent can petition for a change of school. The district has very few conditions that result in an automatic transfer. A move into the new school's catchment area is one. I think that once a child has attended in a specific area for a few years they can remain in that school even if the family moves out of the area. At least that was the case with my granddaughter.
I urge you to contact the district office to learn what can be done before spending more time focusing on this issue. You can get some information from the district's Web site. I suggest you need more information about the school's and the district before you can make an informed decision.
As to your question about lunch and recess times. Students had a combination lunch/recess around noon. There were two different lunch periods with the older students having different times. There were a 15 minute am recess and a 15 minute afternoon recess for younger grades. I volunteered for the lunch time recesses. I also volunteered in the library and for field trips. I felt a part of the team because I knew some of the teachers and staff and was aware of their attitudes toward education and how they fit with school policy. I knew that the majority of the staff were committed to helping students learn.