Some comments/observations:
Clearing time in fresh, unused fixer is going to be quite fast. As fixing by-products accumulate in the fixer with use, that time slows, but the fixer is still doing its job (i.e., completely converting the silver halides into water-soluble compounds). After a certain point, the concentration of silver and other by-products in the fixer is so great that the fixer no longer converts the halides into water-soluble compounds. Sometime before this happens, the fixer needs to be discarded.
The upshot of this is twofold: First, fixer exhaustion should be determined by the amount of dissolved silver in the fixer, not the number of thiosulfate molecules or whatever. In addition, levels of bromide and iodide inhibit fixer activity. The fixer capacity for bromide papers is less than that for chloride papers. T-Max and Delta films, with their higher iodide content need twice as much fixing time and reduce fixer capacity by 50% compared to "conventional" films due to the inhibiting influence of the iodide. Fixer dilution, therefore, plays little to no role in determining the working life of a fixer.
In addition to this, some materials can tolerate more dissolved silver in the fix and still be fixed adequately. Film and RC paper can deal with more silver in the solution than fiber-base paper. Therefore, what's being fixed plays a significant role in the determination of fixer capacity. Add to that the "degree" of fixing needed or desired and capacity numbers can change even more. There are different levels of fixation for fiber-base paper in particular, generally referred to as standards for "commercial use" or for "optimum permanence," etc.
Also, when using a fixer to treat as much film/paper as possible in a given volume, fixing times need to be based on the time the nearly-exhausted fixer needs to do the job, not the clearing time in fresh, unused fixer. Certainly, we could test and come up with a time for the initial batch of film or paper through the fix, and then test for times for subsequent batches, but that seems overly precise and much more trouble than it's worth. Finding a time or time range that works well for the fixer at the end of its useful life seems much more convenient, all other things being equal. The longer times given by manufacturers represent this.
And, while the test for clearing time is a useful guide for when to discard film fixer, it is less useful for determining fixing times. Yes, you test your fix, find 2x the clearing time and then fix your next roll of film for that time and pretty much be assured that the film is fixed adequately. However, if you do a test for clearing time for a liter of fix, double that, and then fix the next 15 rolls of film in that fix for that time, you're almost certainly going to underfix the last several rolls. Batch size and how close the fixer is to exhaustion play an important role here. Furthermore, while doubling clearing time should contain a certain safety factor (although I don't know this for sure, I've never tested how much past "clearing time" is needed for adequate film fixation) it's still a "minimum" time. Extending fixing time for everything but fiber-base papers has almost no disadvantage and can provide a welcome safety buffer. M. Gudzinowicz in his paper, "Post Development Processing," recommends for films either twice the clearing time in two fixing baths or simply using an extended fixing time of 5 minutes in each of two baths in order to "avoid problems and provide some security." This, for conventional films, rapid fixer, and a two-bath fixing regime!
Fixing fiber-base papers for optimum permanence is another can of worms entirely. Two-bath fixation and being sure to use the fixer to less than capacity is really the best insurance here. Even the good old tests for residual silver won't detect some retained by-products (Gudzinowicz again). Skimping on time and/or overusing fixer for this is simply not wise and a quest for fixer speed, to me at least, seems counter-productive. I'll leave the Ilford archival sequence for paper vs. longer fixing and washing times discussion for another thread
Best,
Doremus