Is there any experience with developing a digital strategy and roadmap based on business capabilities in a systematic approach? What successes have you had? What obstacles should one look out for?

Definitely this is a tough one. So, you should start with a clear vision of what the business looks like in the next five years. what are they trying to achieve? what are the metrics and goals in place?
that will give you the first "business capabilities" draft.
then, you start designing what tools or solutions may be required to enable the business capabilities. what the overall requirements will look like?
that will give you the first digital "goal" vision.
Once you have those 2, you start from positioning yourself in the current technology/solutions spot (As-Is) and then start asking what needs to change from this to start moving to the goal vision? and you will need to repeat this step 3-5 times. that will give you an overall steps map.
so, the digital strategy is a combination of a list of IT solutions that will enable the business capabilities. the IT solutions should be evolving as the business is evolving (so the steps map) will help you identify what can be done in what timeframe and what capabilities will it be supporting.

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Having done this a couple times in my prior life, the one thing that can make or break the transformation is how well you answer the question "What are the top 3 business outcomes we want to measurably improve in the next 12 months and how will we know we’ve succeeded?

If you are not able to clearly articulate the answer to this questions and get everyone's buy-in, the transformation is very likely to fail. In the absence of clarity to business value, it becomes a technology-first initiative with no real benefit. 

Yes, we have a framework to assess factors which influence outcomes - helping identify differentiating capabilities (to do more of) and non differentiating capabilities (to optimise/automate/do less of). This has helped my customers prioritise initiatives for growth and accelerate value creation. The framework replies on assessing impact of a capability on consumption of service by user. For example, a chatbot interface which prompts and compares options can help customer to make a choice, usually results in more Buy decisions (growth)

A technology feasibility assessment is a critical first step in evaluating the enterprise's current digital ecosystem, defining gaps, analyzing digital capabilities, completing business requirements gathering, and architecting data and systems integration. The next step is to complete an operational readiness assessment. Despite the tools and resources available, top-down support and organizational cross-functional governance are vital to carving a path forward.