Skip AA on this one
I had to fly into Palm Beach and AA's sole route was via Dallas. Considering I started in Toronto, that was a trifle circuitous, so I flew to MIA and drove up, in 90 minutes or so - thre's also the Metro Rail thingy which is like $4.
The price you quote seems quite high - how long and when (dates) ? Often off-season NetsAAvers are in the $200 range.
Otherwise there are Aeromar, Lan Dominicana MIA - SDQ and then you drive or WHY. I don't know that either go to STI or POP.
Out of curiosity is MIA- SDQ cheaper than MIA - POP /STI for the same time? There are more flights, maybe that's an option.