Ilford Hypam is an ammonium thiosufate based rapid fixer with no hardener incorporated. It works great with pyro because it does not contain a hardener. A non-hardening sodium thiosulfate based fixer will work equally well with pyro - just a bit slower.
Don't know about Ilfostop but I would have thought just about any stop bath would have been OK in the correct dilution. When I first used a staining developer, the article I read said that a good wash for the film was sufficient and would obviate any stain reduction through the use of another chemical, to wit, the stop bath. It is a habit that I have got into and use plain water rinses with agitation whatever developer I use !
An acid stop bath is not desireable and not needed with staining and tanning developers ("pyro"). Acidic solutions can reduce the stain.
A plain water rinse is fine - and it arguably increases fixer life.
Some workers use an alkaline fixer as a one-shot immediately post development (they add fixer concentrate directly to the used developer - post development).
Post development I use a brief water rinse, followed by an alkaline fixer (TF-4).