Are these EMI noises?
You did the right thing: Conducted the null-experiment where you touch the probe tip to the ground connection. Right there you know that the signals you see are picked up by your probe setup. And you are right in thinking it's related to the loop size formed by the ground lead (try muffling around the ground lead and see the signal amplitude change).

The first thing to do is to repeat the measurement using the small spring-clip as a ground lead instead of the long "pig-tail".

To reduce the levels, maybe verify that you need to do so first... So conduct a better measurement as described. And a shielded cable maybe a really good idea if you need that signal to go anywhere useful. SMA is one possible connector.

Next idea may be to hunt for the source of the 640kHz (or 320kHz). Very likely related to the power supply somehow. 

Also, did you design the system with very low power distribution network impedance across the frequencies of interest? (See my pdntool.com and similar resources for help on this)