Hi Julie, welcome from Hampshire.
I completed the SWCP 4 years ago. I did it in sections mainly of 2 or 3 day weekends. I found it was possible to achieve this by using bus services and a little car manoeuvering. It's a wonderful and spectacular walk, and I'd love to be able to attempt it again in one go in the future. The problem with that though is finding 6 weeks to do it in.
The Jurassic Coast Challenge is indeed very tough, and way out of my league. I could walk it at my own pace, but would never be able to meet the set deadlines. Of course, it's doable, but would need some serious training to achieve it.