Good idea, we get lots of Scandis visiting South Florida, especially in the winter. Most of them fly Continental from Oslo via Newark, then to MIA or FLL.
Lately guys have been traveling on Condor from Norway to Frankfurt, then to Fort Lauderdale. Some have tried Air Berlin but said it was a bad experience.
Others have used KLM, most folks search price and buys the cheapest ticket and don't care whether they have to stop and change planes.
The perfect airplane for Oslo to Miami would probably be a 757, long enough legs to fly non-stop, and with 188 seats it is medium size.
(What does SAS fly these days? A-340 and or 330?)
Better rethink that one Towerdog, at 4119 nm OSL-MIA is almost a 1000 nm beyond what a 757 does on a good day with around 180 pax.