Today had to be a better day. Granted, yesterday wasn't totally bad, but it could have been better. Still, I needed some success.
I called the radiator manufacturer today. I had a good chat with the representative. He assured me, that they sell thousands of radiators, and he had never heard of this problem. He offered to send me new connector pieces for the ones I gummed up so far. And he offered advice on using teflon tape, seven to eight wraps around the threading should do, I only used three or so.
The root of the problem most likely lies in the fact that the threading of the connector pieces to the radiator is BSP (British standard pipe), as opposed to NPT (national pipe thread). The BSP thread in this case is a straight thread, whereas the NPT thread is tapered. You can read on Wikipedia what that means.
Regardless, I wrapped, and wrapped, and wrapped (repeat eight times) the teflon tape around the connector piece, and screwed it in nicely. Et voilà, it worked, and again, and again, and again. Quickly hook up the thermostat and fire up the boiler. Well, it was almost too warm to use heat today, a whopping 62°F, but this will change, and we'll be ready.
Time to bring out the champagne, no wait, that just froze to death in the fridge ... ;-)