Yes the methylene blue stain is very easy to use, and is good for "live" exams. Iodine is really only good for fixed specimen, as it degrades cells quickly in live samples.
Methylene blue is also used to treat certain protozoal infections, but will turn the whites of your eyes blue. I don't recommend using it without the direction of a clinician.
I doubt you would have giardia if the labs have eliminated it twice.
As for the E. Hystolytica, which I have had before, your symptoms would have hospitalized you by now, if it was a serious infection. But, having chronic infections with this bug is not outside possibility, if it has made significant adaptations to your body's immune defenses and established a type of equilibrium with your cytokine triggers. In this case it would be considered a true parasite as opposed to the status of pathogen.
It is my feeling, (and I say this without all the necessary background work) you may have a combination of problems going on, which can contribute to susceptibility to one or more "types" of parasites\pathogens. Some may come and go, where other might stick around until your next serious illness (usually a virus, which can boot these things out).
My biggest suspicion in general is: there are complex organisms that have not been catalogued, and next to nothing is known about them. They could be virtually invisible, or move in multiple phenotypes using quorum sensing to form complexes which contribute to the development of higher forms (in the body). They can then disassemble during treatments, or immune assaults, then reassemble when the coast is clear!
I am using certain experimental methods to exam this possibility with myself.
Pretty certain some cancers are a direct result of these types of parasitisms.