Just a few things (mainly as personal opinion/experience)
1) There are many things that can be taught under CAF Familiarization. The nature of these lessons may be the same but the content is "cadet-ized". For example - field movements and cam and concealment can directly to translate to moving along a route and why things are seen. A practical exercise absolutely could be to have cadets move silently to an objective without being seen and record and report observations. (With that said, having that objective being defined as an enemy MG nest and cadets conducting a full scale platoon attack would be crossing a line - particularly for a problem solving exercise).
2) CAF familiarization must be conducted by a person who holds the qual within the CAF. This is a great way to engage your affiliated unit. You will find that once you introduce a couple switched on Cpl/MCpl reservists, with a clear plan, the cadets will literally forget officers exist.
3) Keep in mind that the focus of problem solving is to identify and solve a problem through a process. If you want something that inherently writes itself, ask them to identify an issue at the unit and come up with a plan. (Ex. Recruitment needs to be improved, retention issues, bullying, etc.) This approach will engage the cadets at their level with things that they understand and that directly impacts them.
I think the recycling program example is a little bit off-base, particularly when there are many examples that both cadets and staff can understand from a shared view of inside the unit. If you look at solving a local problem, you may actually find out about problems you never knew existed.
4) SMESC can be an excellent complimentary training for problem solving, because the reality is that problem solving requires planning.
Situation (Problem)
Mission (Solve the Problem)
Execution (How we will solve the problem)
Service Support (What tools do we need to solve the problem)
Command and Signals (What role will people play in solving the problem)