Maybe my workflow can be of use.
I use Hypam or Rapid Fix 1+9 for two minutes each bath. I fix in bath one, wash, dry and collect prints for toning. A toning session is then water soak, fixing bath 2 (always fresh fix) and then straight into the toner with no intervening wash. The only time I have ever got staining is when the fixer was exhausted.
After toning, it's into the wash aid, again without a rinse, for ten minutes with agitation, then into the washer for an hour. After this, all my prints pass residual silver and hypo tests with flying colors.
Note that the HCA and wash before toning is not necessary. It is definitely necessary afterwards, however, since toner also contains fixer.
Finally, I stabilize with Sistan and dry face-up on screens.
Staining comes from residual silver in the prints (i.e., inadequate fixing) or a pH that is too acid. I can't imagine that your prints are too acid after HCA and wash, so the fixing stage comes immediately into question.
Make sure you are not over-using your fixer and extend your times somewhat. That should fix your staining issue.
An aside: selenium toner can also be used as a down-and-dirty test for residual silver. If the print stains, the fixing is not adequate. When you selenium tone, you have a kind of built-in residual fixer test. Your prints seem to have failed
Best,
Doremus
www.DoremusScudder.com