Let me give you my limits of knowledge on the topic.
If this is the Honda 5 speed (which I think it is), Honda retrofitted an oil jet for a design defect. This solved that evolution of issues. The next to appear was pressure switch failure. Most issues encountered by the post oil jet refit or OEM assembly line version were traced to this failure point. No mechanical problems were highlighted if the switches were replaced. More importantly, the owner had to know that the switches should be replaced. Often it was an automatic swap out for a re-manufactured trans ($$$).
Yes, Honda does not recommend a fluid exchange, but has never given any authoritative rhetoric as to why not. This is not wise. They've never stated the purpose of the more wasteful and labor intensive process, and perhaps that is why, it's more labor intensive. Each manufacturer has their dealer incentives. There is absolutely no "harm" to doing a fluid exchange, and the advantages of the more cumbersome method are not apparent. But if you feel compelled to follow that method:
First add Auto-Rx and drive the prescribed mileage. Do a fluid exchange with the cheapest fluid available (probably a multivehicle formula) via cooler lines. Install magnefine at this time. They're a great option in that virtually any end user can install auxiliary filtration. THEN do your conversion to Amsoil via the 3 separate sessions. Again, I think it's totally unnecessary.
As far as Amsoil interfering with the cleaning process, if one were to use Auto-Rx in an automatic with Amsoil or Mobil 1 ATF, I would extend the cleaning about 30%-50% in time/mileage. The deposits in an automatic aren't nearly as serious as they are in the engine that's exposed to the byproducts and direct contact with the combustion process, but this will assure a complete cleaning.
I hope I've answered your questions to your satisfaction. If not, or if you have some new questions, please hit the reply button.