My film fixer is similar to your idea - but I've made it just a bit acid (since I do not use a stopbath - just water.
Kodak Rapid Fixing Bath F-9 (modified)
Water, about 125F (50C) 600 ml
Sodium thiosulfate pentahydrate 360 g
Ammonium sulfate 60 g
Sodium sulfite, desiccated 15 g
Sodium metabissulfite 10g
The paper fixer is TF-2 but with borax in place of metaborate (I don't use a stop also, just water).