MPPT (LT3652) + Solar Panel Voltage
Make sure you are resetting your potentiometer for the different panel configurations as this sets the holding voltage for MPPT. The Sunny Buddy hookup guide refers to a set Voltage of 3.0 V while the schematic refers to a set voltage of 2.8 V. Set voltage is measured from the SET pin to the GND pin. I could see the voltage you are measuring being the same for any number of panel configurations if the MPPT holding voltage is still set at the same voltage. 

'The weirdest thing to us is that with a DC supply, everything works OK. After 6.5V, the circuit "Turns on" ' ... this is interesting since the start-up voltage listed in the datasheet is 7.5 V. Actually reading a little further there is a "Note 4" on page 4 of the datasheet referring to the startup voltage. The note reads as follows...


  Note 4: This parameter [startup Voltage] is valid for programmed output battery float
  voltages ≤ 4.2V. VIN operating range minimum is 0.75V above the
  programmed output battery float voltage (VBAT(FLT) + 0.75V). VIN Start
  Voltage is 3.3V above the programmed output battery float voltage
  (VBAT(FLT) + 3.3V).


This note tells me that your VIN minimum is 4.65 V (4.1 V + 0.75 V) and your VIN Start Voltage is 7.4 V (4.1 V + 3.3 V). If you are currently at 4.485 V that may not be enough to startup or maintain.

Backing up a little Note 3 may also be of interest...


  Note 3: VIN minimum voltages below the start threshold are only
  supported if (VBOOST-VSW) > 2V.


In the schematic VBOOST and VSW are on connected on the battery management side so my guess is that VIN minimums below the start threshold might need help from the battery. Page 12 and 13 of the datasheet elude to this. 

I suggest setting your MPPT voltage per the Sunny Buddy Hookup instructions but use 2.8 V as your set value. Check the voltage across your panel and if it isn't above 7.4 V try to tweak the potentiometer above and below the recommended set point and see if you can measure a VIN value above 7.4 V. Make sure you are measuring good VOC levels to start, such as the 15 V you have achieved in your lab. MPPT will be around 80% of VOC as an approximation...from what I've read.