
Consumer Reports and Good Housekeeping have tested TP disintegration using stirring bars and beakers. The Sweet Home used a different procedure. The three have reached somewhat inconsistent conclusions with some types. All rated softness and other features, as well. I decided to do my own test with a stirrer to focus on varieties I'm interested in.
I liked the old Charmin Plus. By the time I realized it had been replaced with Charmin Sensitive, a two-ply type, the Plus was gone from the shelves so I had to switch. I only have a couple of rolls at this point that I've stuck on a shelf and not used. Charmin Sensitive is fine when used but Good Housekeeping found that it did not disintegrate (dissolve) well. The Charmin products were generally rated poorly for disintegration by all sites, except (possibly) for Charmin Basic, a single-ply variety that did not score tremendously well for softness.
I have tried a couple of papers that Consumer Reports rates well for softness and not awful for disintegration. I don't define softness the same way, apparently. I did not like White Cloud Ultra Strong and Soft (White Cloud USS) very well at all. I bought a pack of it and gave most of the rolls away. Then I tried Cottonelle Ultra Comfort Care (Cottonelle UCC). It's expensive and not rated very highly for disintegration (except for The Sweet Home, which thought it disintegrated well).

I also included White Cloud USS, Charmin Ultra Strong, and whatever two-play 600 grit sandpaper the office puts in the dispensers. I filled a 1000 ml beaker with 800 ml of water and set the stirrer at the same speed for each trial. I did varying numbers of trials for each brand; I should have done about 30 of each then calculated means and 95% CIs, but what I did was good enough for my purposes--I only did a couple of trials for the office paper and Charmin Ultra Strong. I stopped the timer when the paper was in pieces; occasionally a trial failed when the paper got under the stirring bar, preventing it from rotating.
The results were interesting. I expected the Charmin Plus (the old one-ply variety) to dissolve the fastest, and it did: about 6 seconds on average. Next was the office sandpaper, at 7 seconds. Cottonelle UCC came in at 9 seconds, and both White Cloud USS and Charmin Sensitive clocked in at 13 seconds. Charmin Ultra Strong was also about 13 seconds.
The treatment the paper got in the beaker with stirring bar is much harsher than what it'd get on its way to the septic tank from the toilet. I may try a static test next, with no agitation. However, the relevant statistics are not necessarily the times themselves, but the comparisons of one type to another. Cottonelle UCC was 50% slower than Charmin plus but the other Charmin and the White Cloud USS were 44% slower than the Cottonelle UCC. The slowest papers had disintegration times that were more than double that of the fastest.
So in a practical sense, what does this mean? The potential for septic tank clogging is a product of two things: disintegration and amount of paper used. In the latter aspect, Cottonelle UCC may be better than the others I've used (Charmins Plus and Sensitive), which did seem to require more sheets than Cottonelle UCC.
That's about as far as I want to take this. There are tradeoffs and I'm only willing to go so far for septic system health.