sorry for the late reply - i just noticed the question
i did a lot of digging into the various parasite tests a couple of years ago
the labs had variable reputations, different technologies, and pro's and cons
i was particularly interested in single celled parasites - like blastocystis and amoeba
the conclusion i came to that the standard parasitology labs via microscopy for worms and eggs / cysts were very much hit and miss
in the end i selected a test called GI-MAP
it tested for all the parasites i was interested in via PCR which really should be the most sensitive method as it should be able to detect minute amounts of parasite dna in the stool - even if there are no whole organism present that would be visible by microscope
also the test measures other useful markers - like gut inflammation - antimicrobial resistance and and general balance of the microbiome ( another can of worms...so to speak )
https://www.diagnosticsolutionslab.com/tests/gi-map