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work on his EF issues with work that wasn't rote practice of stuff he'd mastered but with stuff that was challenging him? She argued that he had problems tackling even open ended tasks that he could extend to his hearts content such as story writing. ... I feel he needs the nurturing environment of elementary school...
It seems the teacher may be conflating the actual EF issues with an imagined lack of LA content mastery.

While parochial schools which do not accept government funding typically do not need to adhere to the same laws/rules/regulations as public schools and therefore may not create an IEP or 504, it seems that your child's school tries to be supportive. Therefore they may agree to collaborating with you in creating a plan to help address your son's EF issues in school, in a consistent manner with how you prefer to address these issues at home. For the elementary environment to be truly nurturing, they would be seeking positive ways to help your son identify and eliminate behaviors which do not serve him well... not just overlooking such things or pointing them out at a conference without throwing him a lifeline or supportive path for making changes. You may wish to create a list of specific skill deficits such as emotional regulation, decision making, task initiation, persistence. Then create a list of strategies such as learning emotional vocabulary and using words to express one's self rather than crying, creating lists and/or checklists, acceptable fidgeting such as doodling, etc... there is a broad range of possible strategies, milestones, and measures for mastery.

It seems likely that if a plan was in place to provide supports for your son to learn the self-talk skills needed for executive function, agreement on higher level LA curriculum (and/or acceleration) may quickly follow.

There is much information easily found online for strategies to support EF function, and books for children as well. These may make a great starting place in supporting your child and assuring him he is not alone in having trouble learning and consistently demonstrating EF skills.

Wishing you all the best.