Well, I'm pretty confident that I don't know what it is that I'm doing. But I'm trying.
In an effort to try to force an earlier 5-4 downshift, I went to
Transmission > Shift Scheduling > On-Power > Normal/Normal Fault/Cold/Cold Fault/Tow-Haul/Tow-Haul Fault and changed the cells in the 0% and 13% columns to the same values that are in the 25% column just to see if that made a difference. This would be changing the 875 rpm Output Shaft speed to 1600 rpm in all of those tables.
To increase hysteresis, I went to
Transmission > Torque Converter > Flex Apply/Release > Output Speed vs. Throttle > D/S6 and to the 5th App and 5th Rel tables. In the Apply 5th Gear table, I tested increasing the 0% column value by 5, 10 and 15%. Not decerning an improvement, I reset the table back to stock. In the Release 5th Gear table I tested lowering the same column the same percentages, but was not able to notice an improvement. I was not able to be sure in what way to change TPS hysteresis, so I didn't try anything.
Trying to disable Flex-Lock for that gear, in
Transmission > Torque Converter > Flex Apply/Release > Output Speed vs. Throttle > D/S6 I changed all the values in the Apply and Release 5th Gear tables to the same values that are in the Apply/Release 6th Gear tables as that gear is not suppose to utilize Flex-Lock. Unfortunately there was no change in behavior.
Interestingly, the oscillation appears in 3rd through 6th gears. I'm rather mystified.