The 2 labs that I know of do PCR DNA type tests in their enteric panels Metametrix and Diagnos Tech. PCR tests are offered by some labs for some internal Protozoa but the tests are sometimes negative if the person has too few parasites. I don't remember if you have consulted a parasitoligist, some people have written that they were helpful.
The people who do the usual stool parasite exams will report all the organisms they can identify. They are usually well trained in stool preparation but if they see something which 'sort of' looks like a parasite but they aren't able to confirm that it is a parasite they probably wouldn't report it. Many microscopic bodies 'sort of' look suspicious but usually aren't a parasite.