There was a detailed exploration of launching from heavy planets in the Space Exploration Stack Overflow; I think it's a better explanation of the problems with conventional rockets than the cited paper.
Nuclear engines get around the problem because they can give more energy, hence a higher velocity, to the exhaust stream than a chemical reaction can. Unless they have an accident, they don't make the exhaust stream radioactive in the process. So the keys to reducing the radioactive contamination of the launch site are (1) fewer accidents and (2) less radioactivity from accidents.
Fewer accidents is hard. Starting a space program without accidents is almost unbelievably hard. There are likely to be some.
But reducing the radioactivity has some promise. What makes a reactor dangerously radioactive is, well, the reaction in the reactor. The original fuel load isn't so bad, particularly if the fuel is encapsulated in rods or pellets. The radioactivity builds up as the fuel "burns" because it's (mostly) the fission products. So the nuclear engine starts as not so dangerous, but becomes more so as it runs. You'll want to get it launched and on its way.
If you can get your experimental rockets headed out over an ocean, you'll also minimize the problems from eventual explosions. Big chunks will sink, and smaller dust will be dispersed. Oceans are big.
We ended up blowing up a lot of equipment, infrastructure and people getting to space. If there was an easier way, we would have taken it, but there wasn't. So long as a culture on a heavy planet thought getting there was worthwhile, using nuclear rockets isn't that much harder than our progression from throwing things, to firework rockets, to modern chemical rocket engines. It's just one more step.