Tomorrow we meet with the head of special Ed and our sons teacher to start this journey.
He has been diagnosed with sensory integration issues and sub threshold unspecified ADHD.

We just had him moved to a new class with a teacher that cares. He is in trouble for touching other students, making noises (sometimes because he needs to, sometimes for attention). Talking and being off task. He also has social interaction issues, and appreciates older peers who can talk more on his level, and has zero tolerance for smaller children. It's a long school day for a child like our ds, and he comes home overstimulated and tired.

So ds IQ test was not very successful last time, and the psych specialized with children with development issues, but not gifted. P

So if our DS is truly gifted and bored, how do I advocate for him getting help for his boredom with no proof? DS has yet to count to 100 verbally, but has already learned all the goals for the school year. He is very much interested in science, and he craves info. He also keeps making up words because he wants to speak Spanish, or "the language of Egypt". How do I get this kid help in a public school? What tests do I want? I need specifics.

If you don't have a valid IQ test showing gifted you might nit get very far given the other issues.

I know that the district here claims that once the child is in the average range academically that they have no further responsibility to do anything other than what is offered in the general ed classroom. The average range starts at the 16th percentile.

If a child is identified as gifted (using the CogAT in 3rd grade and the cutoff changes every year it seems), then at the beginning of the year the classroom teacher and the parents make a plan to challenge the child in the area of giftedness (apparently one can only be gifted in reading and math). These plans usually include being allowed to use a computer program for math (like EPGY) or reading more difficult books for book reports. No differentiated instruction and no acceleration.

I wouldn't bring up giftedness in this meeting. You're going to need evidence--testing, obvious academic success in the classroom, something--or they're just going to blow you off (they may try to blow you off even if you have all the evidence in the world; in our district the only "evidence" they'll accept is the CogAT which is not very reliable at identifying gifted kids, especially 2E ones).

I'd keep the topic of the meeting focused on how the teacher can help your son with his sensory and attention issues in the classroom (and any therapies he might receive) and then give it a few months to see if things are better. In the meantime, you can research your school's policies on differentiation and acceleration and what the status is of their gifted program.

Oh, and above all, never use the word "bored" with school personnel!

Good luck!