Please understand that there is no single absolutely right way to process prints. The term "archival" has an exact scientific meaning that is too abstract to be practical, but in general it means processing in a fashion that leads to the longest possible life of the final print.

That said, I use a process that is quite similar to yours - developer, stop, quick fix (ammonium thiosulfate in a single bath, "film strength"), rinse, hypoclear, tone in dilute selenium, hypoclear, wash, dry. The only essential difference is that I do use an acid stop, but I dilute it more than the normal recommendation.

Incidentally, the traditional rationale for selenium toning is archival permanence, but the recent book by Tim Rudman argues that unless the print is fully toned in selenium (to the point where there is a noticeable color change), the degree of archival protection is actually quite limited. On the other hand, brief toning in dilute selenium tends to lead to slightly deeper blacks, and slightly cooler tonality - effects that I often want in my prints.

Also, to be exact, hypoclear doesn't actually "wash out" fixer (or toner). Instead, it converts the thiosulfate into a form that can be more easily removed by the water wash that follows. The reason for the second hypoclear treatment is that selenium toner itself contains ammonium thiosulfate.

You will find published recommendations in a lot of good references, including Ansel Adams' books, to take a print directly from the fixer to the toner. My experience is that the risk of staining in the toner increases dramatically if the print is not rinsed and neutralized in hypoclear before being toned.