46re Odd Shifts

You're not missing anything.
What you're experiencing is how, in all of Chrysler Engineer's wisdom, has done to improve mileage.
However, those transmissions are very sensitive to fluid. If +4 is not used, you could run into a lot of annoying stuff. Also too, there's a lot of little filter screens in the system, if there's any blockage in these screens, it could cause issues.
The reason you're experiencing changes in operation related to temperature, is because the TCM's shift strategies are different while in closed loop. Once the trans temp reaches 100°, the TCM goes into the programmed strategies, therefore different feel.
While I was working at a Transmission shop, and also drove an 2001 RT Dakota, I tried tirelessly to solve the Lock-Up right after 3rd apply without success. It would invariably cause a code, and the TCM would go into Limp Mode. Hugely annoying. Chrysler's TCM has a complicated, and often redundant feedback loop that is constantly looking for confirmation of applied elements.
I am not aware of any Flash to get away from this.
The TFOD-Jr is a decent kit, but I used the TFOD kit almost exclusively when the customer agreed to using one.
In all other cases, I would drill specific feeds in the transfer plate that made the trans work really well. Aside from the strategies from the TCM.
@TrailBeast has 20 yrs of transmission experience also, maybe he has a different prospective and maybe offer the Magic Bullet :)