Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
Search segment-by-segment at ba.com. LAN flies MIA-PUJ a few days a week, so that might work for you, but aa.com will not show award availability on LAN metal, and ba.com is not so good about displaying connections on award searches.
Unfortunately, if you cannot find low-tier award seats on your dates of travel, your options are to pay cash, or to book AAnytime awards with your Aadvantage miles.
If you can split your party, try searching for two seats, and then for one seat on a different routing.