Yes, I´m Using DEMOJM with a JM16 daughter board 
The problem is near to be resolve I feel, I´ve disconnected VrefH and you know what the MCU says? it doesn´t care!! O.o
The MCU continues to take VrefH from the "Unknown"
I believe that there we have the reason of the "noise"... cause it´s ignoring the voltage reference supplied!
I forgot to tell before where the signal data comes from, it cames from a 12V battery 3.5Ah (big battery) and through resistors I arrive to 4V (just for testing) the reality is that a geotecnic sonde take that power (12V) and returns as a Current font of 0-20 mA, with that current and 0.1% tolerance resistance I obtain 0-4V.
For testing I use a resistive Divisor, so the NOISE of the data signal barely exists, around +/- 1mV.
I tried stop mode succesfully as you described but... only for 1 sample, I take 1 sample... manually click and get another... and even worst! because not only the values seem to has the same noise... after taking 4 o 5 samples the ADC don´t answer, and the IRQs of the ADC doesn´t enter. I ve tried with a bucle taking 2 samples, it can do it once, but not more, if the bucle is (i<50) forget it, it doesnt work. The sample rate of the ADC is controlled by this bucle, and when the ADC finish then it can continue. To control the sample rate, I can use the RTC, but cause I´m using wait mode (works nice) I´m afraid by IRQs cause the awakening. As I thought that a quick way for slow the sample rate was to do a sub-bucle (from 0 to 50000) doing nothing. But the results was the same.
I believe that:
the MCU is not the problem.
GND is not the problem.
Data signal is not the problem
The problem is... VrefH which I have disconnected, and see with the multimeter pin45 in the daughter card for see if it´s really disconnected... and it marks 0.03V. Fantastic, now the MCU has not VRefH, jaja
But , when running the ADC doesn´t care, he still works with 5V as VrefH.
Im soldering directly to the daughter card instead of using the motherboard, so I can be sure that pin 45 has 0 volts...
Well, PE documentation say this, but when I look for the pdf to see if pin45 is VRefH I realize that the pdf of the JM16 doesnt include the 64 pin package, fantastic. Only 32-48 pin package, so how is possible I have a JM16 64 pin package...
The real problem is, where is VrefH, is it taking from VDDAD directly? The pdf, says that 48 pin package still mix AVDD & VREFH in the same pin, Is it good idea to insert a voltage reference to the AVDD directly?
Voltage reference can not give more than 10mA... but maybe the ADC it´s taking the reference from there...
Im going to see if my MCU exists in the datasheets ... ¬¬ and later post a solution, cause in this moment I don´t know where this MCU cames from, maybe from Jupiter or who knows! with a ghost pin called VrefH... lol