Better way to change colours on gradient tool?

[RocketBoots]

So I have a gradient, and I want to simply use an exact copy of an existing colour on it. Ideally I’d just like to be able to quickly drag the colour swatch onto the gradient - simple, job done! However, the current method required is to select colour picker, drag it over the area of the gradient I want (the big circular swatch right next to the eye dropper icon isn’t pickable), attempt to pick the colour (this is fiddly and often isn’t an exact match), hope I’ve got it, click the colour swatch next to the icon to apply it. This is an even longer process if there is another shape above the one with the gradient - I often make shadows with shapes using a multiply transparency, as can be seen on the canister. 
 

Is there a better way to do this that I’ve missed?

[BarKeegan]

Do you set up Document Palettes in your Swatch settings? It helps me when I want to continuously sample a particular set of colours