Looking at the balls that you had success with, I'd generally stick with symmetrical cores or weaker asyms. The shift is neither. I also would deal with pearl reactives or fairly mild solids. The shift and the secret certainly do not fit this criterium.
I personally would opt for something in the fire or agent lines that has the reactor pearl cover. In the Agent line, the origional agent is the only ball that has the reactor cover. It has that cover and a fairly strong symmetrical core. In the fire line, the fired up and the spit fire have the reactor. They use rather similar cores, but the flip cap on the core switches sides. This makes the Spit fire slightly stronger overall with more hook in the midlane and slightly less on the backend.
All of these balls would work with the Agent being the strongest overall, and the Fired Up being the cleanest through the fronts with the most left on the backend. I would choose the Spit Fire though as a compromise between the other two. You can cut the ball with a strong pin around 4 or 4 1/2 inches to pap, but I would take care not to make the pin to low as you spoke of the other two bowling balls reving up too soon. Granted, the GP2 is a huge hooking ball and the One is no slouch as far as strength, but never the less I'd make sure not to leave the pin any lower than 2" above the midline, especially if you opt for the agent the balls that you spoke of.
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