If my experience is anything to go by, they were probably woody before they bolted.

I don't think anyone knows what is necessary to be able to grow unwoody radishes that don't bolt. It seems you either have suitable ground for growing radishes or you don't. And in my case a large amount of compost added over the years to turn the ground into humus rich ground doesn't see to be sufficient of change to get over this. Nor does the ideal growing conditions of this year's wet spring.

Radishes are fairly promiscuous and will cross with other radishes, and maybe with some other brassicas if they are closely enough related. So if you want the seed you need to apply the appropriate pollination hygiene arrangements to prevent cross-pollination. In my opinion, that's what I pay seed companies to do. I'm told you can eat radish seed pods, maybe that's the best thing to do. I just pulled mine all out and chucked themon the compost heap.