try the charter airlines
I'm coming to DR in December. I also had a bad time finding a good flight. Even the expensive ones had 15 hour layovers in various cities. I would have had to travel for about 25 to 30 hours to get from Minneapolis to anywhere in the DR. If I lived in Miami or New York, I would have had a better selection. Still, they were all expensive; $700+.
I ended up flying from Chicago to SDQ for about $350, on Spirit Airlines. If I had been more flexible on my dates, I could have had a $287 round trip. This made it cheaper than my February flight to Cozumel. The other reasonable flights were on Jet Blue or Ryan International Airlines. Anything on the major airlines was out of the question.
Spirit also has a portal/hub in Fort Lauderdale. If you are in the Miami area, it might be a better option for you.