Warning, nerd content below.
I went ahead today and measured the viscosity and surface tension of the black ink using the approximate method suggested by PeterBJ and authored by Grandad35. The results were pretty interesting, showing as always why it's better to have measured values rather than just speculation.
Again, all values are approximate because the method of measurement is pretty simple and neglects some parameters, but it should be close enough for our purposes.
First I measured the black ink dilution which is working for me now -- OCP BK797 diluted 75% ink / 25% water.
Viscosity: 1.81 centipoise
Surface Tension: 36 dynes/cm
Next I measured the full strength black OCP ink, purchased last week:
Viscosity: 2.36 centipoise
Surface Tension: 31.7 dynes/cm
Since I was having this same problem with my old batch of ink, which was purchased in a large quantity in late 2010, I decided to measure it too. So this is OCP black, full strength, and a 4 year old batch:
Viscosity: 2.18 centipoise
Surface Tension: 29.7 dynes/cm
Finally, to give a reference point, I measured one of my 'darker' inks which has never given me any problems, OCP Red R122 (this was from the 4 year old batch, for what it's worth):
Viscosity: 1.95 centipoise
Surface Tension: 29.25 dynes/cm
What can we say about these results? Well, for one, the viscosity difference I was expecting to see with the black ink is real, compared to the OCP red. (I chose OCP red as the 'reference' ink because, by eye, it appears to be the thickest of the colors that have never given me any issues. This should be verified too.)
Also, the surface tensions of the new and old black inks are quite close to each other, as well as to the red ink. This explains why adding Formaflo didn't seem to help at all (in fact after 15 test pattern prints it seemed like things were getting worse).
The diluted black ink, which I mixed at 25% water to 75% ink as a stab in the dark, is now less viscous than even the red ink. However, the surface tension is increased, because of my adding water to it (water has a comparatively high surface tension).
I found a couple papers online that had methods for calculating viscosity and surface tension of two-part solutions, and made an Excel workbook to calculate these parameters based on the percentage of water used to dilute. If anybody is interested in it I can share it. Using this, it calculated a theoretical value of 33.6 for surface tension and 1.85 for viscosity of my diluted black ink. This is surprisingly close to the measured values of 36 and 1.81.
One step further, if I wanted to roughly match the values of the red ink: again using my spreadsheet, it looks like if I use 20% water in my black ink I'll end up with ~33.1 and 1.93 for surface tension and viscosity. These values are pretty close to what the red ink measured. I can't reduce the surface tension without adding some Formaflo, and I think the value is probably close enough without it.
One thing I don't know is if the printer handles all colors equally while printing, in terms of nozzle firing. If not, then matching the parameters of my trouble-free red ink might be the wrong approach. The best would be to get another OEM Canon black tank, and see what it measures, and then try to match that.
Josh