Just about all of the aftermarket radiators come with the auto trans cooler connections. I run a Modine radiator on my G-prod Civic (11:1 compression, mild cam, close ratio box) and it cools just fine...in fact I sometimes have to add tape to my grill to get the water temps high enough.
I don't use the A/T connections. I did plug them to keep moist air out to minimize possible corrosion, and to prevent a potential leak source if the radiator decided to crack and leak internally into the A/T cooler section.
Regarding the factory oil cooler that sandwhiched between the block and the filter... You can upgrade DX blocks to the Si set up quite easily. I used to run this set up for many years on my ITC car. When I upgraded to Prod, I added an external cooler. I now run a cooler-less DX set up and just run with a big external cooler, since I needed a bigger cooler anyway (the small amount the factory cooler helped was much less effective with the prod setup, so I ditched it). My other reason for getting rid of the factory cooler is that it is a potential failure point. You have two coolant lines that can fail/leak, plus you have the cooler itself that can fail internally causing the oil & coolant to mix. So on the recommendation of the guys at King Motorsports, I got rid of it.
There is one area that the factory cooler is extremely helpful. Technically, it's not a cooler, but rather it is a heat exchanger. It will exchange heat from the hotter temp fluid to the colder fluid. Normally, we think of the oil as being hotter (my typical oil pan temps are around 220-230 so it's a reasonable assumption) with coolant temps in the 170-180 degree range. However, during cold start-up, the coolant heats up much, much faster than the oil. So the factory cooler does help to preheat the oil during warm-up. Now this probably doesn't help road racers, (typically after 1 lap, my temps are good to go) but I suspect it would help a Solo II car greatly, since their runs are so short, I would bet that their oil is just getting to a good temperature about the time that they have finished their runs.
I am also quite amazed at how good Honda engineering is. When I converted my engine to Prod, I looked at the old rod bearings when the new bottom end was being assembled. While the old engine ran for about 4 seasons and had a lot of race miles on it, the bottom end still looked like new. I also like the fact that Honda's for the most part, generally don't leak, provided you run the OEM gaskets in critical areas (pan and valve cover for example) and you don't screw up when you install them. Keep clean oil in them, keep the temperatures under control, and Honda's run forever!