Have you talked to the kindergarten? I think that you should also get information from the other side as to what they expect, where they feel he is and how he would integrate into the classroom now vs later. I think without speaking to the other school, you are not getting the full picture. The school should also have resources for an evaluation (my DD has an apt. with the speech pathologist at her ES) and be able to tell you if he might be better served doing therapy with them in K or remaining in preschool and doing OT therapy privately.
My sister started 1st grade in a new school after our parents split up the year before, at the end of K. The K teacher suggested sis be held back in K because she was shy (she had just been through a huge life change, duh). My mom addressed her concerns to the new school and they said they would put her in a mixed "pre-first/first" grade classroom and see how she did. If she struggled, then she would take 1st grade later. (It was the district's solution to kids who would be retained in K without making them do K exactly). My sister did fine, but since the school had a head's up they were able to select her class, her teacher, and monitor her more closely than they might a different child. My sister will never be a social butterfly. She's very introverted. But she's a smart, successful person in her own right.
If being told more than once means a child isn't ready for K, then very few children are ready and don't get me started on selective hearing in teenagers!
I think you need more information to decide if holding him back is the right thing or not. From here, I'm not sure why you can't go forward and work on things in kindergarten. My friend is keeping her son in preschool one more year, but he's right at the September cut off, not already 5. So, I don't think another eval would be a bad thing, but I would contact the ES about it. They should have resources for you, even for a possible incoming K student. At this point, my DD has aged out of the early childhood programs and I was directed to her school.