Southwest publishes much lower rates than the numbers it sounds like you've been quoted by Delta:

http://www.swacargo.com/swacargo/doc...20Rates_v2.pdf
http://www.swacargo.com/swacargo/doc...ed%20Rates.pdf

For general freight, it looks like it would be between $4.00 and $4.75 per kg (about $1.80 to $2.15 per lb.) from various parts of the continental US to Punta Cana, with about a $100 minimum. For next flight out rush service, a 23-45 kg package (about 50 to 100 lbs.) would be $355 to $415.

I haven't dealt with them, but I would expect add-on fees for document preparation, customs clearance, etc.