First question is, is this really ripple (from your upstream power
source) or is it oscillation within the regulator itself? The upper
traces look unlike usual power supply ripple, which tends to be
more triangular than sawtooth. The duty cycle on a switcher
would have to be pretty narrow to get that kind of ripple. So I
am inclined to think that you have a relaxation oscillator on your
hands, under some confitions, and a generally unstable loop
since I see not one flat (or nothing-but-noise) yellow line in
the bunch.
Using a true DC source (battery stack) would put the question
of incoming ripple and its attenuation or gain, to bed.
A current limit too low on the incoming supply, is one way to
get a relaxation oscillation in power circuits.