We have found the schools to be very challenging, sometimes it seems like mass dysfunction at every turn and it's almost impossible for parents to navigate the situation.

I recommend doing some research on comprehensive evaluations for special education. What normally happens is that the school suggests an eval or the parent puts in a request. Then within a certain timeframe you are supposed to get a prior written notice stating what they are going to do for the evaluation. I think what this includes can vary but we got a list of specific tests that they were planning. Once the parent signs the plan the school has a certain time limit to finish the eval, you meet, and they go through the eval results and tell you whether or not he qualifies for an IEP or a 504 plan. In terms of this eval, they have to report on the child's cognitive ability. I am not sure whether they think the OLSAT is an acceptable test, but I think that's poor practice. In one district we were in they use the CogAT for special ed students, which is really not meant for the purpose of evaluating students with possible disabilities and they adamantly refused to do a real IQ test. In the district we are in now, we had CogAT results and they adamantly refused to even discuss them (even though they were high) in DS's latest IEP eval basically saying the results are meaningless in terms of assessing cognitive ability. They ended up using outside WISC results that we had from a neuropsych but if we hadn't had that, they would have given him the WISC. You may be able to google search evaluation manuals that come out from the Department of Ed for your state and see what kinds of testing they tell districts to do.

Also, I think it would be a really good idea to pursue outside testing. We went to a neuropsych as well as getting private occupational therapy and physical therapy evals. The private OTs like to use tests like the Beery VMI, and the BOT to assess fine motor ability. The neuropsych gave DS a test called the Grooved Pegboard to assess manual dexterity as well as repeating the Beery VMI. With a combination of those types of tests you should be able to distinguish between a visual-motor issue vs. something else like manual dexterity (or a combination of the two). It sounds like the school OT is just kind of observing him which sounds like the wrong path to go down. The school should be doing actual testing.

Schools will not diagnose dysgraphia. They might report specific results of testing but not actually give it a label. They may diagnose "Disorder of Written Expression" if there is a gap between his cognitive ability and written expression, but that would involve a test like the Woodcock Johnson or the WIAT or the TOWL.

If it's purely a handwriting issue, I don't think he's going to qualify for any services unless you have an outside medical diagnosis which could put him in a category like "Other Health Disability" or "Physical Impairment" (my son's handwriting issue is stemming from Developmental Coordination Disorder).

I'm wondering if what your district is doing is some sort of Response to Intervention rather than an actual comprehensive evaluation for special education. They might claim that they need to do this RtI before evaluating him but when a parent makes a request, they cannot use RtI to delay a comprehensive evaluation.
http://www.wrightslaw.com/nltr/09/nl.1027.htm