Given that this was a roadmap problem, then I don't think it will be necessary to work through any elaborate route. I think practically, if you did the period ate cleavage followed by an aldol, the reaction could give a 50:50 mixture or worse (or better). Given that R and R' are not specified, it would be difficult to predict. If I were doing this in the lab, I would just try it. If the yields were even half good, I'd just stop. (If this were for a commercial product, that would be different.)
Given the symmetry of the intermediate, I think selectivity will always be problematic. The Diels-Alder reaction could be attempted with an unsymmetrical diene. You would still need to think out how this would grant the selectivity needed. I'd put down an aldol and ask your professor if he had something else in mind.