FWIW our school is in the process of abandoning some of the weirder parts of Everyday Math (no more lattice multiplication). But it remains a very wordy, language-y way to learn math, which disadvantages kids who are uneven in their skills, like yours (and mine). I wouldn't put a first grader into 3rd grade EM unless I was sure he could write sentences about how he solved problems, because that's all over the workbooks.
We have not found a perfect solution to the scheduling headaches that come with subject acceleration. Right now DS has language arts separate from his class peers just so he can get math. It's not ideal, but it's what could be worked out.
Can your DS's teacher (or a 2nd grade teacher) change the time when she teaches math, to facilitate your DS getting appropriate instruction?
We have found that in the years when DS worked "independently" (workbook alone in the corner of the class) he got only 1/3 to 3/4 of a year of math instruction at school, the variable being how much the particular teachers that year were invested in his learning. It's unrealistic to expect a 1st grader to teach himself, no matter how much he loves the material.
We have found that having DS in a class with other kids has been important. If we couldn't get that, I would argue for the school providing someone to instruct him as a 1:1 pull-out during the hour when the class has math.
Good luck,
DeeDee