That definitely looks like composite in your first picture where you have captured about 6 individual lines of video, each starting with a sync pulse. However the sync pulses are enormous in comparison to the size of the video brightness information so something may not be right.
Conventionally, composite video inputs have a fairly low terminating resistance of 75 ohms - the input of the scope is about a Megaohm. This means that the composite-out transistor on the Spectrum is not being given a proper emitter load when it is only connected to a scope, so to have a look at the composite-out properly, place a 68 ohm or 100 ohm resistor between the composite signal and ground, and then with the resistor in place, have another look at it on the scope.
Edit: I just caught your latest posts. That's good progress. To be honest Composite from a Spectrum was never the cleanest, that is why I always strove to use RGB instead. Try turning down the color control a little bit, it may reduce that color smearing.
Now that you know where to get composite from, you can try using RGB on Nautilus by feeding composite into its Csync input and of course RGB into the R, G, B inputs. It may be necessary to attenuate the RGB signals if the Spectrum is outputting digital levels on those lines.