Been there, done that. An older inefficient radiator is just that. Moving that coolant through there faster just decreases the dwell time that the fluid has to cool in the radiator.
It won't fix the problem.
Depending on the cooler type, a large oil cooler can restrict airflow through the radiator and of course, it sheds it's heat right into the radiator if it's mounted in front.
Traditional tube & fin coolers allow better airflow through than the newer plate type coolers.
While it can make a nice difference in oil or trans temps, it won't make up for an inefficient radiator. Depending on the climate you live in, it may not be advisable to run an external trans cooler that excludes the radiator completely.
I do agree with the synthetic oil. I run as much synthetic lube in my rigs as I can.
As you have previously pointed out, there are many variables involved, and changing one changes the others. There are situations where a high flow pump will improve the cooling. IN some cases a new radiator helps, in some cases a new, better radiator helps, in some cases a better, new radiator and a high flow (new) pump will outperform one or the other by themselves. I could design a situation where an used radiator would see improved cooling with a high flow pump. It would also see improved cooling with a new radiator. Which is better, depends on the used and new radiator, radiator condition, and the pressure / flow difference in the pumps.
In other words, under the right conditions, better coolant flow will dissipate more heat. Under other conditions it will not. In fact under some conditions, additional coolant flow can cause problems.
The other issue is cost per unit change in performance. Water pumps are less expensive than radiators. That said, in most cases I would change a radiator first, unless it was already new, or it was new POS.
Also if the overheating is at highway speed, I would favor a bigger surface area radiator over a high flow pump (assuming the existing pump is working). If the overheating is at idle, it might be a toss up. If at idle I had a good 40 F delta T across the radiator, I might favor a high flow pump, unless the radiator is partly clogged, and reducing the flow, in which case one should probably deal with the radiator first. If the delta T across the radiator was 20 F at idle, I would be more inclined to replace the radiator with a bigger radiator (more tubes, more area), assuming the fans and clutches are working properly.