I had good experiences with Mudanza Condado from Monte Plata to Higuey, it was 3 years ago, phone number is 809-3790626
They were good, punctual, inexpensive and overal good service.
The truck, packing, unpacking, everything cost about 12.000 pesos (from Monte Plata to Higuey, 200 revenue kms and over 230 dead-heading kms)
The truck was a mid-siozed truck, enough to move a 2BR APT.
They are from Santo Domingo, but can pick up and deliver to any place. Because you would be doing Santiago - SD there should be no problems.