I would not trust an agent to search for upgrade space for you. They are probably trained to do searches in a goal to find you a flight in common ways (ie. shortest duration, lowest price, etc). I would find it highly doubtful that they are trained to help you find an itinerary with the most upgrade availability.

I typically search every hub-destination (and return dest-hub) routing available to look for R space on the days I want. Then I check the origin-hub (and return) flights since these are usually shorter. If I'm lucky enough to find R>0 on all segments, I immediately book and immediately apply GPUs. If R goes to zero, I immediately cancel and repeat