Yes that 11.7v for your morning voltage is way too low for your size of battery bank and the time spent charging them, even allowing for a 6amp draw all night. That is only 60AH.
Usual thing there is the batteries being sulfated so they have way less capacity than you think, so they run down quickly. You can spot sulfation by using an hydrometer to see what the SG is when they are fully charged. Might be 1.250 instead of 1.275
Your prosine has a desulfation program to do 16volts for however many hours. You must disconnect the rig from the batts first so you don't hit the fridge control board with 16v (15.4v limit on that) and any other delicate items. Read the prosine manual instructions before doing it :)
Next, review how they got that way--undercharging and being left below full charge overly long. Follow this guide:
http://www.wholesalesolar.com/pdf.folder/battery-folder/charging_instruction_2011_2.pdf