No pictures here to show how or what I did.
After the second soldering attempt ultimately ruined the wires in a RJ45-DB9 connector, I thought that soldering wires of similar dimension together would allow me to observe how the wires responded to heat. Using the wires I had practiced on the first time, I stripped off some more insulation, separated two from the thick twist, and then twisted those two together. Soldering those two were easy, with successful adhesion.
The second time, I stripped some wires from the CAT5 cable that I was using to "split" one of the wires in the RJ45-DB9 connector. I twisted those individual CAT5 wires, which are thicker than the wires I was practicing on earlier. I then took the CAT5 twist to just one skinny wire from the practice cable, and twisted.
This time, the twisting went much more successfully than the attempt on the RJ45-DB9 connector. The reason is simple: I had greater length of stripped wire to manipulate than in the connector. The longer stripped lengths permitted one-and-a-half to two full twists, permitted a strong connection that didn't seem all that temporary. These longer wires and and superior initial connection also optimized the soldering connection.
Clearly, more stripped wire length is better when it comes to twisting and soldering.
I repeated the experiment with wires of similar stripped length and similar twist. I initially tried being creative with the twisting, thinking that I might get a superior splice. That didn't work, so just holding all three wires together and twisting is the best way to create a temporary splice, so far. Another change was that this time, I just held the soldering iron against the wires, and waited for the remaining CAT5 insulation to melt, burn, or somehow indicate that the heat was causing a change. The amount of time that passed before the insulation began to receded away from the heat source, deforming as it pulled back, was about a second.
This suggests that when I solder my next RJ45-DB9, I should just tap the solder end to the iron, until some solder melts onto the iron, and tap that liquid solder drop to the twisted wires. Pull back immediately, do not wait, and let cool. A system administrator suggested inserting the DB9-pinned CAT5 wires into the end of the DB9 connector, before soldering. That should reduce the risk of breaking the wires even after an otherwise successful solder.