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Thanks for your patient effort with this limited user. 

As I began to work through your careful instructions  I noticed one drawback in the out come which was relatively minor and my design might have absorbed : the colour along the straight edges varies slightly from the top to the bottom as the section that is cut out is at a different angle to the change in colour gradient. 

However, a more critical problem for me is that I need to dictate exactly the start colour and exactly the finish colour which I couldn't figure how to do with your process.

The good news is that your description of the process gave me an idea I thought might solve both those problems and so far almost has done.

I produced a rectangular gradient so I could choose exact start and finish colours. I selected the whole rectangle and under transform and distort I pulled the two ends together to make a right-angle which I had drawn on another layer. That gave me the consistent and defined colour that I need on the straight edges and turned the gradient into the quadrant sweep I was looking for.

A slight quirk is that it has produced a black line over the green and sporadic black pixels down the other two edges which I will either crop off or paint over. 

Thanks again for your time and inspiration.