A quick word about two-bath fixing and fixer dilution:
The two-bath fixing regime depends on bath one to remove the lion's share of the undeveloped silver halides while the relatively fresh second bath finishes up the job. The reason for the second bath to extend total fixer life. With it, one can safely "overuse" bath one (i.e., use it past its capacity as a single bath) by a factor of around four. The less-than-adequately-fixed prints coming out of bath one near the end of its life are still 80%-90% fixed; there are just some insoluble compounds left in them that bath two takes care of. Since bath two hasn't much work to do, it remains fresh enough to serve as bath one when the original first fix has reached its capacity. So, if you can fix 10 8x10 prints per liter of fix in a one bath regime, you can fix, to the same or better level of permanence, around 40 8x10s per two liters of fix, divided into bath one and bath two. If you then promote the second bath to bath one and mix a new bath two, you can fix another 40 prints, but this time you've only mixed one liter of fix, making things really economical.
The recommendation to use "film-strength" fixer for fiber-base paper is based on the idea that the resulting shorter fixing time will keep the fixer and contaminants from soaking into the paper base and thereby facilitate more rapid and efficient washing. Ilford espouses this method of fixing. Note that Ilford's method requires the use of a wash aid (a good idea in any case!). Without it, wash times would likely be significantly longer.
The problem with two-bath fixing and strong fixer with a one-minute total fixing time is that it is difficult to fix for exactly 30 seconds in each bath, especially with larger prints and longer drain times. And, if one exceeds the 60-second total time, the fixer soaks more into the paper base and requires more washing. IIRC, 90 seconds is about the time it takes to fully saturate the paper base with fixer, so there's not much leeway.
I find it easier to fix with "paper-strength" fixer when using two-bath fixing. The times are longer so the paper base gets saturated and requires a longer wash time. Still, once the paper base is saturated, a few extra seconds in the fix doesn't make any difference to the wash time. I use Ilford Rapid Fixer or Hypam at the 1+9 dilution for 1.5-2 minutes per bath. If I need a little extra drain time, I don't worry, and, since I transfer prints directly from the second fix to the toner, I like to make sure they are well-drained so I carry over as little fixer as possible to the toner.
Note that the fixer capacity does not change for the two dilutions. Fixer capacity depends on the build-up of by-products, not exhaustion of the fixer compounds itself. A stronger dilution gives shorter times and vice-versa. With two-bath fixing and "print-strength" fixer, there is even more economy and fixing is not compromised.
TF-4 should be able to be used in a similar way.
Testing your fixing regime isn't difficult at all. Use the selenium toner test or Kodak ST-1 to test for residual silver (adequate fixing) and the Kodak HT-2 test to test for residual hypo (adequate washing) Test once to find the limits of your regime, add a safety factor and then test the last print through the fix each session regularly as a control.
Best,
Doremus
P.S: Thanks to Matt for correcting my misinformation about the selenium toner test for residual silver in post #20.