I've been looking more into what sort of training is recommended and there is a lot about doing mostly really easy runs as these may make your body adapt better to running. You still need some workouts for speed and strength though. Some of the routines I've seen are about improving your 5k, but so far I've not seen one that actually includes doing a weekly parkrun. I feel I need an intervals run as well so that would leave a couple of easy runs (zone 2 heart) with one of them being long. I am going to try that for a few weeks. I'll fit in some strength work at home too.
That said, I'm interested in how your training goes. 20 minutes would be amazing.
I'm also interested in those easy run strategies, I think you just have to go with feel a lot of the time! Let me know how it goes!