GSM/GPRS antenna noise depending on cable length and position
Something to try:

Adjusting the cable length and antenna mounting seems to affect the noise you are measuring, but that doesn't necessarily mean that the noise is coming from the RF. When the cable length or counterpoise (adding aluminium sheet) changes, the load (complex impedance) presented to the output of the RF module will change. This can cause the amplifiers in the RF module to consume more or less current. I would suggest disconnecting the 4V LDO and try powering the RF module from a bench top supply while the rest of the board is powered normally. Make sure you use low impedance connections (thick cables) for the power and ground connections between the bench top supply and the RF module. If the problem goes away then you are dealing with a power delivery problem.