Not sure, if it will be interesting for anyone, but in Salsita a few months ago we started using on our internal project and I wrote down our experience.
There are two things that can be somehow interesting for people here:
We are unfortunately not using Basecamp for project management. We tried to use Shape Up using GitHub Projects. We even tried to somehow recreate the Hill Charts. tl;dr We used two boards - one that was managed by the team and the second one that has columns that were mitigating different stages at the Hill.
For the shaping phase, we used a Design Sprint. I feel that it can work well if you don’t have 100% clear idea, what you want to do. Since Design Sprint is very well structured, it can help you better understand the problem and investigate viable solutions.
If you’re interested, you can read the blog post here: https://blog.salsitasoft.com/shape-up-practical-lessons-from-the-first-cycle/
Since we are a software agency, the biggest hurdle is how to sell this “unusual” methodology to our clients. We are now trying Shape Up on one of our client project. But I would be interested to know other tips and experiences on how to sell Shape Up to clients.