I haven't tried borax, and in fact I just got lucky with the original HC-110 monobath, in that I eyeballed the amount of ammonia needed to offset the acidity of the rapid fixer. Ammonia has some other disadvantages, though; it would probably produce high fog with any other developer than HC-110 or possibly Ilfotec HC.
Another potential option would be crystalline sodium thiosulfate and ammonium chloride, mixed in the correct ratio in place of commercial fixer. That produces a pseudo-rapid fixer that does better on tabular grain films than plain thiosulfate. This could be used with a powder developer -- like D-23 that hasn't been mixed into the water yet. I've even heard that you can buy crystalline ammonium thiofsulfate, though it's apparently so hygroscopic that it's hard to keep it from deliquescing.
Some old books mention that a large amount of potassium bromide can be used with ammonia solutions to prevent fogging during development. HC-110 may already contain enough anti-fogging agents.
I guess that mix a weakly alkaline developer solution with a rapid fixer (containing ammonium thiosulfate) might cause some ammonia to evaporate, resulting in a slower but usable sodium thiosulfate/ammonium thiosulfate fixing mixture, similar to sodium thiosulfate/ammonium chloride. Adding ammonia can not only increase pH but also increase the concentration of ammonium ions, thereby enhancing the fixing speed. As you mentioned, ammonium thiosulfate is difficult to store and is usually sold as a 60% solution or as a concentrate for rapid fixer here.
Ps.a formula based on ammonium thiosulfate, I heard that it can complete development and fixing within 10 seconds, but I haven't tried :
- 6g of sodium sulfite
- 3g of hydroquinone
- 1g of phenidone
- 2.5g of potassium hydroxide
- 12ml of 60% ammonium thiosulfate
- Add water to 100ml.
The use of a large amount of phenidone, high pH, and ammonium thiosulfate together seems reasonable, but it feels like there might be significant ammonia evaporation and not stable.