Need good example of two domains involving different procedural knowledge yet sharing same high-level strategies
I think "teaching of high-level strategies will allow students to use learned strategies across different domains" is the very rationale of mathematics. Math gives very good examples of both abstract strategies for solving problems across different domains and also specific, explicit strategies. You don't seem to want the abstract strategies, but if you change your mind on that, George Polya's How to Solve It is one of the best books on this topic. 

Your other constraint is that the domains should be simple, otherwise differential equations or graph theory would be great examples of explicit solution strategies having applications across multiple domains. 

I guess something that will meet your needs well is linear algebra and, in particular, solution strategies for systems of linear equations.