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 :)

It has +4 and has since it was rebuilt. That was part of the reason it was cooked, before I got it, the front pump seal went out and the previous owner dumped Dex/Merc in it since that was cheapest. Took about 3 hours to fully clean the transmission and components. I'll see if I can find a link to the flash bulletin. I went with the Jr since this truck doesn't pull much, and when it does it's not a heavy load. It's just a daily driver quad cab Dakota.

OD is fed its apply fluid only through the 3rd gear circuit, meaning it may already be trying to go into OD as soon as or right after 3rd applies.
The speed sensor and computer are responsible for that.
Also keep in mind that when fluid changes temp it changes viscosity and that affects pressures, which in turn affects what the computer sees and reacts to.
This explains why it works different cold to hot.