So how I did it, I will probably never know. I'm home again now, after a full 20 minute run with zero stops and zero walking, and an additional 5 minutes of huffing and puffing extensively, and a face like a blotchy tomato, but somehow I made it through. This is the hardest thing I've done for and to myself in probably 15 years. I almost cried at the end and phoned my mum, screaming "TWENTY MINUTES! TWENTY MINUTES!" until she could finally make out what I was saying.
Thanks to all before me who posted their W5R3 success stories - you are what made me believe I could do it too.