How about a show like they have on HGTV where you have 2 candidate leads and a team. They are given a problem to solve or something specific that needs to be built, and each lead candidate has to develop a plan and then present it to the customer. This includes costing and novel approaches.
The customer chooses the lead who presented what they feel is the best solution.
The next quarter of the show is montages of the team building it, and the final quarter is the presentation of the results and customer response.
I think web sites or apps would be good for this type of show, since they have a visual element. People watching the show get a feel for the whole cycle, including project management.