Without adding a shift kit to boost the pressures the extra length and friction on the added cooler circuit is questionable. Thats the real problem with doing it as the current system, flow, and pressures are designed for what is there with no additions. The return flow form the cooler directly cools and lubes all the thrust washers, planetaries, and the main drive train pieces of the transmission. Any reduction there has some real downsides. I definitely would not an extra cooler without removing the drainback check ball and highly recommend a shift kit to boost the pressures and flow.
The routing of the fluid to the cooler or back to the sump is controlled by a shuttle valve that has prest pressures fro the flow in the transmisison. In fluid coupling only about 10 psi of the available pressure is routed thru the cooler. That goes to 50 psi when the TC locks. Obviuosly TC locked is the more desirable condition for cooling. While you really can't chnage the psi on the shuttle valve the higher pressures equate to high flow thru the system so you do get a boost in cooler flow with a shift kit. That helps cool things better and allows adding extra cooling without impacting flow.
That is why a lot of people add the manual lockup switch to override in conditions where it is needed, like low speed high load conditions where you can maintain a constant speed. Doesn't work well at all in stop and go traffic but is more intended for crawling out of campgrounds on switch backs or slower gravel roads out of remote areas.
By manually selecting a gear then locking the TC you can mitigate a lot of heating problems if you encounter the above situations. You are correct, you really don't want to shift locked to locked as that is pretty hard on the stock trans. If you need to shift out the manual selected gear unlock the TC then lock it again.
The heat exchanger is the first component in the cooling system after the fluid leaves the trans. It is done that way beacuse it is the most efficienct at removing heat, the fluid to fluid coolers are somewhere in the 90% range of heat transference in a pretty small package. The air to fluid coolers like what is out front are 10 imes larger yet are only about 40% effective at transfering heat in the fluid. Even though the heat exchnager is using engine coolant at engine temp of around 190 degrees it will still bleed a lot of heat out of the trans fluid. It is no unusual to see 230-240 degrees at the fornt cooler output line in a hard pull. The heat exhanger will pull that down to somewhere around 200 degrees and the front cooler, given enough air flow, will take another 40 degrees off the fluid temp. Cooing the trans driven train and bushing will add another 20-30 degrees back so you see pan temps in the 190 range as the desired point. That is in lockup mode. In fluid coupling most of the fluid is dumped to the sump for use in the TC so it doesn't get cooled. You have 230-240 degree fluid being dumped uncooled into probably a 1/4 or less cooled fluid by volume in those conditions. Easy to see why pan temps skyrocket when the TC is unlocked.
Even with a fan on a fluid to air cooler it just will not overcome the heat generated in certain circumstances. In reality, an aux cooling system probably should have its own pump and circuit into and out of the pan for the best effect. That way you don't mess with the trans lube circuit. The downside is another pump, lines, and wiring to install\maintain.